1. Lecture 9 (1) Physics in Life Sciences Fluid flow in human body2

2. Do you know You have 80,000km of blood vessels B747: Nonstop flight for 100 hrs

3. Flow: the movement of fluid particles. At different locations in the stream the particle velocities may be different, as indicated by v 1 and v 2.

4. Steady flow : the velocity of fluid particles at any point is constant as time passes. In steady flow, the pattern of streamlines is steady in time, and no two streamlines cross one another.

5. Unsteady flow - Turbulent flow is an extreme kind of unsteady flow and occurs when there are sharp obstacles or bends in the path of a fast-moving fluid Unsteady flow : the velocity of fluid particles at any point of the fluid changes as time passes.

6. Compressible or incompressible flow Compressible flow : the density of a fluid varies as the pressure changes - gases are highly compressible. Incompressible flow: the density of a fluid remains constant as the pressure changes - liquids flow in an incompressible manner. Compressible or incompressible flow Compressible flow : the density of a fluid varies as the pressure changes - gases are highly compressible. Incompressible flow: the density of a fluid remains constant as the pressure changes - liquids flow in an incompressible manner.

8. The mass of fluid per second (e.g., 5 kg/s) that flows through a tube is called the mass flow rate. Conservation of mass flow : If a fluid enters one end of a pipe at a certain rate (e.g., 5 kilograms per second), then fluid must also leave at the same rate, assuming that there are no places between the entry and exit points to add or remove fluid. The mass of fluid per second (e.g., 5 kg/s) that flows through a tube is called the mass flow rate. Conservation of mass flow : If a fluid enters one end of a pipe at a certain rate (e.g., 5 kilograms per second), then fluid must also leave at the same rate, assuming that there are no places between the entry and exit points to add or remove fluid.

10. EQUATION OF CONTINUITY The mass flow rate (  Av ) has the same value at every position along a tube that has a single entry and a single exit point for fluid flow. For two positions along such a tube  1 A 1 v 1 =  2 A 2 v 2  = fluid density (kg/m 3 ) A = cross-sectional area of tube (m 2 ) v = fluid speed (m/s) SI Unit of Mass Flow Rate: kg/s EQUATION OF CONTINUITY The mass flow rate (  Av ) has the same value at every position along a tube that has a single entry and a single exit point for fluid flow. For two positions along such a tube  1 A 1 v 1 =  2 A 2 v 2  = fluid density (kg/m 3 ) A = cross-sectional area of tube (m 2 ) v = fluid speed (m/s) SI Unit of Mass Flow Rate: kg/s

11.  1 A 1 v 1 =  i A i v i

12. Cholesterol and Plugged Arteries A clogged artery In the condition known as atherosclerosis, a deposit or atheroma forms on the arterial wall and reduces the opening through which blood can flow.

14. Doppler flow meter to measure the speed of red blood cells. To locate regions where blood vessels have narrowed. 5MHz In the carotid artery in the neck, blood flows three times faster through a partially blocked region than it does through an unobstructed region.

15. The ratio of the radii is A 1 v 1 = A 2 v 2, (  1 =  2 )

17. Circulation

18. Honey drop (viscous flow)

19. 1.Water drop - nonviscous flow-all fluid particles across the pipe have the same velocity 2.Honey (or blood) drop-A viscous - does not flow readily-different layers have different velocity. 1.Water drop - nonviscous flow-all fluid particles across the pipe have the same velocity 2.Honey (or blood) drop-A viscous - does not flow readily-different layers have different velocity. Pipe

20. Lamellar flow Why do we have viscosity? Internal resistance It is due to Internal resistance

21. With friction or air resistance A roller coaster track PE  KE  PE+Heat Stop here Energy form A  Energy form B + thermal energy

22. The flow of a viscous fluid (blood, honey) is an energy-dissipating process. The viscosity hinders neighboring layers of fluid from sliding freely past one another. A fluid with zero viscosity flows in an unhindered manner with no dissipation of energy. An incompressible, nonviscous fluid is called an ideal fluid (water). The flow of a viscous fluid (blood, honey) is an energy-dissipating process. The viscosity hinders neighboring layers of fluid from sliding freely past one another. A fluid with zero viscosity flows in an unhindered manner with no dissipation of energy. An incompressible, nonviscous fluid is called an ideal fluid (water).

23. The viscosity of a fluid is described by the coefficient of viscosity  SI Unit of Viscosity: Pa · s Laminar flow

24. The viscosity  of the fluid Due to the viscosity, P 2 > P 1

25. In order to maintain a constant velocity, a force F should be applied. v = 30m/hr Friction F Air resistance

26. The volume flow rate Q (in m 3 /s) of the viscous fluid: a difference in pressures P 2 - P 1 must be maintained between any two locations along the pipe in order for the fluid to flow. And Q ~ P 2 - P 1 a long pipe offers greater resistance to the flow than a short pipe does- Q is inversely proportional to the length L. Q is inversely proportional to the viscosity . Q being proportional to the fourth power of the radius, or R 4. The volume flow rate Q (in m 3 /s) of the viscous fluid: a difference in pressures P 2 - P 1 must be maintained between any two locations along the pipe in order for the fluid to flow. And Q ~ P 2 - P 1 a long pipe offers greater resistance to the flow than a short pipe does- Q is inversely proportional to the length L. Q is inversely proportional to the viscosity . Q being proportional to the fourth power of the radius, or R 4.

27. the viscosity  of the fluid POISEUILLE'S LAW A fluid whose viscosity is , flowing through a pipe of radius R and length L, has a volume flow rate Q given by POISEUILLE'S LAW A fluid whose viscosity is , flowing through a pipe of radius R and length L, has a volume flow rate Q given by

29. Graph of blood pressure vs time in a major artery

31. Viscous and non-viscous flow Physics of viscosity POISEUILLE'S LAW Blood pressure and circulation