1. Circuitry of cardiovascular system and structure-function relationship
Dr. Shafali

2. The functions and design of the cardiovascular system are, in many ways, similar to that of a water utility in a modern city. A water utility is tasked with distributing clean water to its many consumers. The distribution network is vast, and pumping stations are required to ensure that water arrives at sufficiently high pressure for adequate flow from faucets and showerheads . Waste water is collected and returned to treatment plants under low pressure by an elaborate system of drains. The cardiovascular system similarly distributes blood at high pressure to ensure adequate flow to many consumers (cells). Waste (venous) blood travels back to the heart at low pressure for “treatment” by the lungs. Water utilities distribute water, a Newtonian fluid whose flow characteristics behave predictably under pressure. The cardiovascular system circulates blood, a viscous non-Newtonian fluid comprising water, solutes, proteins, and cells. Considerable pressure must be applied to blood in order to make it flow through the vasculature at rates sufficient to meet the needs of the tissues. The capillaries used to deliver blood to individual cells are extremely leaky, unlike the copper pipe used in household water-distribution systems. Leakiness means that the pressure used to drive flow through the system also drives fluid out of the vasculature and into the intercellular spaces. Lastly, the pipe-work used to distribute and collect blood from cells is composed of biologic tissue that stretches and causes the vessels to distend when pressure is applied. Distensibility poses a threat to system function because there is always the potential that the entire vascular contents might become trapped in the pipes, thereby allowing the vascular faucets to run dry.

3. Learning Objectives
Describe the organization of the circulatory system and its function
Explain how the systemic and pulmonary circulations are linked physically and physiologically
Understand the relationship between flow, velocity, and cross-sectional area

4. Learning Objectives
Understand the relationship between pressure, flow, and resistance in the vasculature .
Define resistance and conductance. Understand the effects of adding resistance in series vs. in parallel on total resistance and flow.

6. Functions of circulation
Supply the tissues with nutrients
Removal of waste product of tissue metabolism
Control blood flow to the skin and limbs to regulate heat loss
Aids in body’s defence mechanisms by delivering antibodies ,platelets and leucocytes to the affected area of the body.

7. General features of the cardiovascular system
The cardiovascular system consists of two pumps (left and right ventricles) and two circuits (pulmonary and systemic) connected in series.
When circuits are connected in series, flow must be equal in the two circuits.
Cardiac output is the output of either the left or right ventricle, and because of the series system, they are equal.
Also, the chemical composition of pulmonary venous blood is very close to the chemical composition of systemic arterial blood, and systemic mixed venous blood entering the right atrium has the same composition as pulmonary arterial blood.

9. The aorta and large arteries recoil between ventricular con-tractions, continuing the flow of blood to the periphery

11. 120

12. Vascular system is broadly divided into high pressure system (>25 mmHg) – responsible for control of systemic arterial pressure and distribution of blood flow.
Low pressure system (<25 mm Hg)--- responsible for control of blood volume and venous return

13. Cardiac output and heart rate of the two circuits are equal, so stroke volumes are the same.
Despite this, all pressures are higher in the systemic (peripheral) circuit. This shows that the vessels of the circuits are very different. The systemic circuit has much higher resistance and much lower compliance than the pulmonary circuit.
The lower pressures mean that the work of the right ventricle is much lower.
In addition, the lower capillary pressure protects against the development of pulmonary edema

14. Pressure in the aorta is high and it decreases toward the right atrium.
The pressure dissipates, overcoming resistance. The amount of pressure lost in a particular segment is proportional to the resistance of that segment.
There is a small pressure drop in the major arteries (low-resistance segment); the largest drop is across the arterioles (highest resistance segment), and another small pressure drop occurs in the major veins (low-resistance segment).

15. NORMAL BLOOD PRESSURE IN DIFFERENT PORTIONS OF CIRCULATORY SYSTEM

16. Local arteriolar dilation decreases arteriolar resistance, which increases flow and pressure downstream (more pressure and more flow get downstream).
Local arteriolar constriction increases arteriolar resistance, and flow and pressure decrease downstream

17. Types of blood vessels
Windkessel vessels/Distensible vessels- aorta ,pulmonary artery and their large branches.
Resistance vessels– arterioles ,metarterioles and pre capillary sphincter.
Exchange vessels—capillaries
Capacitance vessels- venules and veins
Shunt vessels or Thoroughfare vessels/A-V shunts
Windkessel – means elastic reservoir ; with ageing these vessels loose there elasticity , thereby SBP increases and DBP decreases as extra blood leaves the aorta very rapidly. This results in increased pulse pressure ( SBP- DBP) Resulting in defective perfusion at the periphery.
Skin and skeletal muscle blood vessels represent by far the most important site of peripheral resistance and offer max resistance to blood flow.

19. WINDKESSEL (DISTENSIBLE) VESSELS (large arteries)
Highly elastic
Windkessel means elastic reservoir
During systole they distend withstanding the high systolic pressure
Once systole is over they recoil contributing to the diastolic pressure

21. BLOOD DISTRIBUTION IN DIFFERENT PARTS OF CIRCULATORY SYSTEM

22. COMPLIANCE OF BLOOD VESSELS
The compliance or capacitance of a blood vessel describes the volume of blood the vessel can hold at a given pressure. Compliance is related to distensibility and is given by the following equation: where C ,Compliance (mL/mm Hg) ,V Volume (mL), P Pressure (mm Hg)
The equation for compliance states that the higher the compliance of a vessel, the more volume it can hold at a given pressure.
The degree to which a distensi-ble vessel or container expands when it is filled with fluid is
determined by the transmural pressure and its compliance.
Transmural pressure(PTM) is the difference between the
pressure inside and outside a blood vessel

23. For each type of blood vessel, volume is plotted as a function of pressure.
The slope of each curve is the compliance.
Compliance of the veins is high; in other words, the veins hold large volumes of blood at low pressure.
Compliance of the arteries is much lower than that of the veins; the arteries hold much less blood than the veins, and they do so at high pressure.

24. Compliance is essentially how easily a vessel is stretched.
If a vessel is easily stretched, it is considered very compliant. The opposite is noncompliant or stiff.
Elasticity is the inverse of compliance. A vessel that has high elasticity (a large tendency to rebound from a stretch) has low compliance.

25. Blood volumes of various elements of the circulation in a person at rest.

26. Blood Volume
The largest blood volume in the cardiovascular system is in the systemic veins.
The second largest blood volume is in the pulmonary system.
Both represent major blood reservoirs.
The systemic veins and the pulmonary vessels have very high compliance compared to the systemic arteries; this is primarily responsible for the distribution of blood volume.
strechibility

27. CHARACTERISTICS OF SYSTEMIC VEINS
Systemic veins are about 20 times more compliant than systemic arteries.
Veins also contain about 70% of the systemic blood volume and thus represent the major blood reservoir.
In the venous system, then, a small change in pressure causes a large change in venous volume

29. Example-Hemorrhage Cause venous pressure to decreases.
Because veins are very compliant vessels, this loss of distending pressure causes a significant passive constriction of the veins and a decrease in blood stored in those veins.
The blood removed from the veins will now contribute to the circulating blood volume (cardiac output), a compensation for the consequences of hemorrhage.
The sympathetic nerves innervating the veins will cause an active constriction and a further reduction in stored blood volume.

30. Volume loading (infusion of fluid)
Increases venous pressure. The increased pressure distends the veins; this is a passive dilation.
The volume of fluid stored in the veins increases, which means that some of the infused volume will not contribute to cardiac output.
The large volume and compliant nature of the veins act to buffer changes in venous return and cardiac output.

31. Because of the high compliance of veins, large increases of pressure occur mainly with substantial increases of volume, as in congestive heart failure, or with massive sympathetic activity that reduces compliance.
Similarly, substantial decreases of central venous pressure occur with large loss of volume.
An exception is the effect of posture, which can lower central venous pressure, even though blood volume has not changed.
This is because gravity causes blood to pool in the dependent veins.
The actual venous return to the heart is determined by the venous pressure gradient.

33. Cross-Sectional Area

34. Velocity of the Bloodstream
Velocity, as relates to fluid movement, is the distance that a particle of fluid travels with respect to time, and it is expressed in units of distance per unit time (e.g., cm/sec).
Flow, is the rate of displacement of a volume of fluid, and it is expressed in units of volume per unit time (e.g., cm3/sec).

35. In a rigid tube, velocity (v) and flow (Q) are related to one another by the cross-sectional area (A) of the tube

36. Total cross sectional area
Because conservation of mass requires that the fluid flowing through a rigid tube be constant, the velocity of the fluid will vary inversely with the cross-sectional area. Thus, fluid flow velocity is greatest in the section of the tube with the smallest cross-sectional area and slowest in the section of the tube with the greatest cross-sectional area. As shown in Figure velocity decreases progressively as blood traverses the arterial system. At the capillaries, velocity decreases to a minimal value. As the blood then passes centrally through the venous system toward the heart, velocity progressively increases again. The relative velocities in the various components of the circulatory system are related only to the respective cross-sectional areas.

37. Volume of blood flow through the CVS is the amount of blood pumped by the heart into the aorta and the same volume is passing through all the segments.
Velocity is inversely related to the total cross-sectional area of all vessels of a particular segment.
Velocity is greatest in the aorta, decreases to a minimum in the capillaries, and then increases from the venules to the right atrium.
Low velocity in the capillaries allows their major function to occur effectively:
exchange of dissolved substances between the plasma and the tissues, i.e., nutritional flow.

38. The average velocity of fluid movement at any point in a system of tubes in parallel is inversely proportional to the total  cross-sectional area at that point. Therefore, the average velocity of the blood is high in the aorta, declines steadily in the smaller vessels, and is lowest in the capillaries, which have 1000 times the total  cross-sectional area of the aorta .The average velocity of blood flow increases again as the blood enters the veins and is relatively high in the vena cava, although not so high as in the aorta

39. Factors influencing velocity
Cross sectional area of segment
Phase – Systolic phase ↑ velocity
Diastolic phase ↓ velocity
Viscosity - ↑viscosity ↓ velocity
↓ viscosity ↑ velocity
Applied physiology
Velocity decreases in heart failure.

40. Velocity of circulation
. Clinically, the velocity of the circulation can be measured by injecting a bile salt preparation into an arm vein and timing the first appearance of the bitter taste it produces The average normal arm-to-tongue circulation time is 15 s.

41. The total pressure within the tube equals the lateral (static) pressure plus the dynamic pressure. The gravitational component can be neglected because the tube is horizontal. The total pressures in segments A, B, and C will be equal, provided that the energy loss from viscosity is negligible (viz., this fluid is an "ideal fluid"). In a narrow section, B, of a tube, the linear velocity, v, and hence the dynamic component of pressure, ρv2/2, are greater than in the wide sections, A and C, of the same tube. If the total energy is virtually constant throughout the tube (i.e., if the energy loss because of viscosity is negligible), the lateral pressure in the narrow section will be less than the lateral pressure in the wide sections of the tube

42. In most arterial locations, the dynamic component will be a negligible fraction of the total pressure.
However, at sites of an arterial constriction or obstruction, the high flow velocity is associated with a large kinetic energy, and therefore the dynamic pressure component may increase significantly.
Hence, the pressure would be reduced and perfusion of distal segments will be correspondingly decreased.
This example helps explain how pressure changes in a vessel that is narrowed by atherosclerosis or spasm of the blood vessel wall. That is, in narrowed sections of a tube, the dynamic component increases significantly because the flow velocity is associated with a large kinetic energy.

44. Q. The greatest pressure decrease in the circulation occurs across the arterioles because (A) they have the greatest surface area (B) they have the greatest cross-sectional area (C) the velocity of blood flow through them is the highest (D) the velocity of blood flow through them is the lowest (E) they have the greatest resistance

45. Q. A 25 year old graduate student while going for her lectures on her power bike skids off the road and sustains a fracture to her right leg. The fractured leg is bleeding profusely. At the ER, her blood pressure is determined to be low. Homeostatic mechanisms in stabilizing the blood pressure will include increases in total peripheral resistance. The site of highest resistance in the vasculature is in the;
A. Arterioles
B. Venules
C. Capillaries
D. Large arteries
E. Veins

46. Q. 12 A healthy 32-year-old woman participates in a clinical study
Q. 12 A healthy 32-year-old woman participates in a clinical study. Her blood volume is 5,200mL. Images are obtained to determine the volume of blood in various vessels in various body positions at rest and during exercise. While lying supine, which of the following vascular structures will most likely contain the largest portion of the total blood volume in this woman?
A. The left ventricle
B. The right ventricle
C. The pulmonary vasculature
D. Veins and venules
E. Vena cavae
F. Capillaries
G. Arterioles

47. BLOOD FLOW
Quantity of blood that passes a given point of circulation in a given period of time.
Units= ml/min
Normal blood flow is – streamline or laminar(Silent)
Random flow in a vessel - Turbulent flow
In laminar flow , the velocity of flow is greater in the center than the outer edges .

48. DEMONSTRATION OF LAMINAR & TURBULENT BLOOD FLOW

49. Axial streaming and flow velocity
The distribution of red blood cells in a blood vessel de-pends on flow velocity. As flow velocity increases, red blood cells
move toward the center of the blood vessel (axial streaming),where velocity is highest. Axial streaming of red blood cells lowers the apparent viscosity of blood

50. Laminar flow is flow in layers.
Laminar flow occurs throughout the normal cardiovascular system, excluding flow in the heart.
The layer with the highest velocity is in the center of the tube.
Turbulent flow is non layered flow.
It creates murmurs. These are heard as bruits in vessels with severe stenosis.
It produces more resistance than laminar flow.
Laminar flow can be disturbed at the branching points of arteries, and the resulting turbulence may increase the likelihood that atherosclerotic plaques will be deposited. Constriction of an artery likewise increases the velocity of blood flow through the constriction, producing turbulence and sound beyond the constriction (Examples are bruits heard over arteries constricted by atherosclerotic plaques and the sounds of Korotkoff heard when measuring blood pressure

51. Blood flow is streamlined until a critical flow velocity is reached
Blood flow is streamlined until a critical flow velocity is reached. When flow is streamlined, concentric layers of fluid
slip past each other with the slowest layers at the interface be-tween blood and vessel wall. The fastest layers are in the center of the blood vessel. When the critical velocity is reached, turbulent flow results. In the presence of turbulent flow, flow does not in-crease as much for a given rise in pressure because energy is lost
in the turbulence. The Reynolds number defines critical velocity.

52. The maximal velocity at which the flow becomes turbulent .
CRITICAL VELOCITY
The maximal velocity at which the flow becomes turbulent .
Expressed in REYNOLDS NUMBER .
R= PDV / 
P= Density of blood (1), D = diameter of vessel , V= Velocity of blood flow (cm/sec) ,  = viscosity in poises
When number is 2000 – TURBULENCE occurs .
Velocity , Cross section eg; Stenosis
Velocity , Viscosity eg; Anaemia
In humans, the critical velocity is sometimes exceeded in the ascending aorta at the peak of systolic ejection, but it is usually exceeded only when an artery is constricted. Turbulence occurs more frequently in anemia because the viscosity of the blood is lower. This may be the explanation of the systolic murmurs that are common in anemia.
The density is a dimension of the molecular weight of the composition. In simpler words, density = number of molecules x molecular weight/volume occupied, while the viscosity is a measurement of the inter-molecular forces and molecule shapes. Viscosity tells you the “friction” amid two layers of the given fluid, while density varies slightly with temperature, viscosity changes rapidly. Both density and viscosity decreases with temperature, but viscosity mostly has an exponential relationship with temperature. Density holds a linear relationship.

53. Decreasing blood viscosity, e.g., anemia Vessel branching
The following promote the development of turbulent flow (i.e., increase Reynolds’ number):
Increasing tube diameter
Increasing velocity
Decreasing blood viscosity, e.g., anemia
Vessel branching
Narrow orifice (severe stenosis)—due to very high velocity of flow
The vessel in the systemic circuit that is closest to the development of turbulent flow is the aorta. It is a large-diameter vessel with high velocity. This is where turbulence should appear first in anemia

54. IN THE CLINIC – turbulent flow
Usually accompanied by audible vibrations, detected with a stethoscope .
When the turbulence occurs in the heart, the resultant sound is termed a murmur; when it occurs in a vessel, the sound is termed a bruit.
E.g- In severe anemia, (1) the reduced viscosity of blood and (2) the high flow velocities associated with the high cardiac output .
Blood clots, or thrombi, are more likely to develop in turbulent than in laminar flow.

55. Shear Stress on the Vessel Wall
Flowing blood creates a force on the endothelium that is parallel to the long axis of the vessel.
This shear stress (γ) is proportionate to viscosity (ɳ) times the shear rate (dy/dr), which is the rate at which the axial velocity increases from the vessel wall toward the lumen.
, for a Newtonian fluid, the shear stress among layers is proportional to the velocity gradient in the direction perpendicular to the layers. The proportional constant or the proportionality factor is the viscosity of the fluid.
Shear stress at the vessel wall also influences many other vascular functions, such as the permeability of the vessel walls to large molecules, the synthetic activity of endothelial cells, the integrity of the formed elements in blood, and blood coagulation. An increase in shear stress on the endothelial wall is also an effective stimulus for the release of nitrous oxide (NO) from vascular endothelial cells; NO is a potent vasodilator.

57. IN THE CLINIC - Dissecting aneurysm
In certain types of arterial disease, particularly hypertension, the subendothelial layers of vessels tend to degenerate locally, and small regions of the endothelium may lose their normal support.
The viscous drag on the arterial wall may cause a tear between a normally supported and an unsupported region of the endothelial lining.
Blood may then flow from the vessel lumen through the rift in the lining and dissect between the various layers of the artery. Such a lesion is called a dissecting aneurysm. It occurs most often in the proximal portions of the aorta and is extremely serious.
One reason for its predilection for this site is the high velocity of blood flow, with associated large shear rate (du/dy) values at the endothelial wall.

58. WALL TENSION
La Place law: States that tension in the wall of a cylinder (T) is equal to the product of the transmural pressure (P) and the radius (r) divided by the wall thickness (w):
T= P r/w
Consequently, the smaller the radius of a blood vessel, the lower the tension in the wall necessary to balance the distending pressure.
Thus, at the pressures normally found in the aorta and capillaries, the wall tension of the aorta is about 12,000 times greater than that of the capillaries. In a person standing quietly, capillary pressure in the feet may reach 100 mm Hg. Even under such conditions, capillary wall tension increases to a value that is still only one three-thousandth of the wall tension in the aorta at the same internal pressure.

60. This property can be explained in terms of the law of Laplace
Because of their narrow lumens (i.e., small radius), the thin-walled capillaries can withstand high internal pressures without bursting.
This property can be explained in terms of the law of Laplace
Wall tension opposes the distending force (Pr) that tends to pull apart a theoretical longitudinal slit in the vessel .
Transmural pressure in a blood vessel in vivo is essentially equal to intraluminal pressure because extravascular pressure is generally negligible

61. The transmural pressure is the pressure inside the cylinder minus the pressure outside the cylinder, but because tissue pressure in the body is low, it can generally be ignored and P equated to the pressure inside the viscus. In a thin-walled viscus, w is very small and it too can be ignored, but it becomes a significant factor in vessels such as arteries. Therefore, in a thin-walled viscus, P = T divided by the two principal radii of curvature of the viscus

62. IN THE CLINIC- Dilated heart
If the heart becomes greatly distended with blood during diastole, as may occur with cardiac failure, it functions less efficiently.
More energy is required (greater wall tension) for the distended heart to eject a given volume of blood per beat than is required for a normal undilated heart.
The less efficient pumping of a distended heart is an example of Laplace's law, which states that the tension in the wall of a vessel or chamber (in this case the ventricles) equals transmural pressure (pressure across the wall, or distending pressure) times the radius of the vessel or chamber.
The Laplace relationship ordinarily applies to infinitely thin-walled vessels, but it can be applied to the heart if correction is made for wall thickness. The equation is σ = Pr/w, where σ = wall stress, P = transmural pressure, r = radius, and w = wall thickness.

63. Estimation of blood flow through various parts of the body
Use of flow meters – (Direct method) In animals Electromagnetic flow meter
Plethysmography
Ficks principle – Also used to measure Cardiac output ,renal/coronary / cerebral blood flow can be estimated
Indicator dilution technique
PAH clearance
By doppler study

64. Plethysmography

65. Poiseuille’s Law Describes the Relationship Between Pressure and Flow

66. In electrical theory, Ohm's law states that the resistance, R, equals the ratio of voltage drop, E, to current flow, I.

67. The flow to an organ such as the kidney, for example, could be calculated as mean
arterial pressure minus renal venous pressure divided by the resistance of all vessels in the renal circuit

68. Poiseuille Equation
The effective perfusion pressure is the mean intraluminal pressure at the arterial end minus the mean pressure at the venous end.
resistance in the cardiovascular system is sometimes expressed in R units, which are obtained by dividing pressure in mm Hg by flow in mL/s

72. EFFECT OF VESSEL DIAMETER ON BLOODFLOW

73. Viscosity
Viscosity is a property of a fluid that is a measure of the fluid’s internal resistance to flow.
Viscosity is the frictional resistance in between the laminae of the flowing fluid .
Frictional resistance is due to red cells and plasma proteins.
The greater the viscosity, the greater the resistance.
The prime determinant of blood viscosity is the hematocrit.

75. In large vessels, increases in hematocrit cause appreciable increases in viscosity. However, in vessels smaller than 100 m in diameter—that is, in arterioles, capillaries, and venules—the viscosity change per unit change in hematocrit is much less than it is in large-bore vessels. This is due to a difference in the nature of flow through the small vessels. Therefore, the net change in viscosity per unit change in hematocrit is considerably smaller in the body than it is in vitro

77. Rate of blood flow  4 th power of the radius
r= radius depends also on the nerve supply(sympathetic causes v. constriction )
= viscosity of blood
Viscosity of blood increases as the hematocrit( cellular component ) increases

78. Q
A 53-year-old woman is found, by arteriography, to have 50% narrowing of her left renal artery. What is the expected change in blood flow through the stenotic artery?
Decrease to ½
(B) Decrease to ¼
(C) Decrease to 1/8
(D) Decrease to 1/16
(E) No change

79. Critical Closing Pressure
This is because the vessels are surrounded by tissues that exert a small but definite pressure on them, and when the intraluminal pressure falls below the tissue pressure, they collapse. In inactive tissues, for example, the pressure in many capillaries is low because the precapillary sphincters and metarterioles are constricted, and many of these capillaries are collapsed. The pressure at which flow ceases is called the critical closing pressure.

80. It is apparent from that the greatest drop in pressure occurs in the very small arteries and arterioles. However, capillaries, which have a mean diameter of about 7 μm, have the greatest resistance to blood flow. Nevertheless, it is the arterioles, not the capillaries, that have the greatest resistance of all the different varieties of blood vessels that lie in series with one another This seeming paradox is related to the relative numbers of parallel capillaries and parallel arterioles. Most simply, there are far more capillaries than arterioles in the systemic circulation, and total resistance across the many capillaries arranged in parallel is much less than total resistance across the fewer arterioles arranged in parallel. In addition, arterioles have a thick coat of circularly arranged smooth muscle fibers that can vary the lumen radius.

81. Hemodynamics - Summary

82. A 56 yr old female is admitted to the hospital for a hysterectomy
A 56 yr old female is admitted to the hospital for a hysterectomy. After surgery, she is transferred to the intensive care unit. Her mean systemic blood pressure is 100mmHg and her resting cardiac output is 4 L/min. Which of the following is total peripheral resistance in this patient?
0.025(ml/min)/mmHg
0.025 mmHg/(mL/min)
40( ml/min)/mmHg
40 (mmHg/(mL/min)
4000 (ml/min)/mmHg
4000 (mmHg/(mL/min)

83. Series Versus Parallel Circuits

85. Parallel

88. 3.6ml/min 45ml/min 90ml/min 135ml/min 160ml/min

89. 0.0625mm hg/l/min 0.05 mm hg/l/min 0.04 mm hg/l/min 0.03 mm hg/l/min

90. A MD 2 student is performing experiments on blood flow in various vessels. She came to the conclusion that the velocity of blood flow is slowest in the capillaries. The most likely reason for this is:
A. Capillaries have the smallest cross-sectional area
B. Capillaries have the largest cross-sectional area
C. Decreased in blood viscosity in the capillaries
D. Single stream of blood flow
E. Decreased in turbulence

91. The circuit below has an inflow pressure of 120 mmHg and an outflow pressure of 40 mmHg. Resistance is each of the vessel shown is 2mmHg/ml/min( R1=R2=R3=R4=2mmHg/ml/min).What is the total peripheral resistance of the circuit shown in the picture below?
8 mmHg/ml/min
4 mmHg/ml/min
2 mmHg/ml/min
1 mmHg/ml/min
0.5 mmHg/ml/min

92. In order to maintain constant flow through a tube with varying diameters, which of the following would be true( where A1 and A2 represent cross sectional areas, and V1 and V2 represents the corresponding flow velocities)?
V1=V2
V1=A1× V2
A2= A1 ×V1/V2
V1=A1 ×A2/V2
V1 ×A2=V2 ×A1