1. California State University, Chico
CE 150 Fluid Mechanics
G.A. Kallio
Dept. of Mechanical Engineering, Mechatronic Engineering & Manufacturing Technology
California State University, Chico
CE 150

2. Elementary Fluid Dynamics
Reading: Munson, et al., Chapter 3
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3. Inviscid Flow
In this chapter we consider “ideal” fluid motion known as inviscid flow; this type of flow occurs when either
1)   0 (only valid for He near 0 K), or
2) viscous shearing stresses are negligible
The inviscid flow assumption is often valid in regions removed from solid surfaces; it can be applied to many problems involving flow through pipes and flow over aerodynamic shapes
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4. Newton’s 2nd Law for a Fluid Particle
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5. Newton’s 2nd Law for a Fluid Particle
The equation of motion for a fluid particle in a steady inviscid flow:
We consider force components in two directions: along a streamline (s) and normal to a streamline (n):
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6. Newton’s 2nd Law Along a Streamline
Noting that
we have:
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7. Newton’s 2nd Law Along a Streamline
Integrating along the streamline:
If the fluid density  remains constant
This is the Bernoulli equation
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8. Newton’s 2nd Law Across a Streamline
A similar analysis applied normal to the streamline for a fluid of constant density yields
This equation is not as useful as the Bernoulli equation because the radius of curvature of the streamline is seldom known
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9. Physical Interpretation of the Bernoulli Equation
Acceleration of a fluid particle is due to an imbalance of pressure forces and fluid weight
Conservation equation involving three energy processes:
kinetic energy
potential energy
pressure work
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10. Alternate Form of the Bernoulli Equation
Pressure head (p/g) - height of fluid column needed to produce a pressure p
Velocity head (V2/2g) - vertical distance required for fluid to fall from rest and reach velocity V
Elevation head (z) - actual elevation of the fluid w.r.t. a datum
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11. Bernoulli Equation Restrictions
The following restrictions apply to the use of the (simple) Bernoulli equation:
1) fluid flow must be inviscid
2) fluid flow must be steady (i.e., flow properties are not f(t) at a given location)
3) fluid density must be constant
4) equation must be applied along a streamline (unless flow is irrotational)
5) no energy sources or sinks may exist along streamline (e.g., pumps, turbines, compressors, fans, etc.)
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12. Using the Bernoulli Equation
The Bernoulli equation can be applied between any two points, (1) and (2), along a streamline:
Free jets - pressure at the surface is atmospheric, or gage pressure is zero; pressure inside jet is also zero if streamlines are straight
Confined flows - pressures cannot be prescribed unless velocities and elevations are known
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13. Mass and Volumetric Flow Rates
Mass flow rate: fluid mass conveyed per unit time [kg/s]
where Vn = velocity normal to area [m/s]
 = fluid density [kg/m3]
A = cross-sectional area [m2]
if  is uniform over the area A and the average velocity V is used, then
Volumetric flow rate [m3/s]:
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14. Conservation of Mass “Mass can neither be created nor destroyed”
For a control volume undergoing steady fluid flow, the rate of mass entering must equal the rate of mass exiting:
If  = constant, then
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15. The Bernoulli Equation in Terms of Pressure
Each term of the Bernoulli equation can be written to represent a pressure:
pgh : this is known as the hydrostatic pressure; while not a real pressure, it represents the possible pressure in the fluid due to changes in elevation
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16. The Bernoulli Equation in Terms of Pressure
p : this is known as the static pressure and represents the actual thermodynamic pressure of the fluid
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17. The Bernoulli Equation in Terms of Pressure
The static pressure at (1) in Figure 3.4 can be measured from the liquid level in the open tube as pgh
: this is known as the dynamic pressure; it is the pressure measured by the fluid level (pgH) in the stagnation tube shown in Figure 3.4 minus the static pressure; thus, it is the pressure due to the fluid velocity
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18. The Bernoulli Equation in Terms of Pressure
The stagnation pressure is the sum of the static and dynamic pressures:
the stagnation pressure exists at a stagnation point, where a fluid streamline abruptly terminates at the surface of a stationary body; here, the velocity of the fluid must be zero
Total pressure (pT) is the sum of the static, dynamic, and hydrostatic pressures
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19. Velocity and Flow Measurement
Pitot-static tube - utilizes the static and stagnation pressures to measure the velocity of a fluid flow (usually gases):
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20. Velocity and Flow Measurement
Orifice, Nozzle, and Venturi meters - restriction devices that allow measurement of flow rate in pipes:
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21. Velocity and Flow Measurement
Bernoulli equation analysis yields the following equation for orifice, nozzle, and venturi meters:
Theoretical flowrate:
Actual flowrate:
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22. Velocity and Flow Measurement
Sluice gates and weirs - restriction devices that allow flow rate measurement of open-channel flows:
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23. Velocity and Flow Measurement
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