Transcript Figure E3.2 (p. 101) Static and Dynamic Pressures
Applications of Bernoulli’s Equation
p
1
V
1 2 2
g p
2
V
2 2 2
g
z
2
p
1 1 2
V
1 2 1
p
2 1 2
V
2 2
z
2
p
2
p
1 1 2
V
0 2 What happens if the bicyclist is accelerating or decelerating?
Figure E3.2 (p. 101)
Static and Dynamic Pressures
• Along a streamline:
p
V
2 2
g
gz
constant p= static pressure, thermodynamic pressure
V
2 =dynamic pressure, it represents the pressure 2
g
rise when the fluid In motion is brought to a stop sentropically.
ρ g z= hydrostatic pressure, not actually a pressure, but represent a change in pressure due to potential energy variations of the fluid as a result of elevation changes The sum of these is called total pressure
Stagnation Pressure
p stag
V
2 2
g
Pitot Static Probe
Connected to a pressure transducer or a manometer to measure the dynamic pressure
Cross-section of a directional finding pitot-tube
For symmetric object, stagnation is clearly at the tip or front For non-symmetric object, stagnation point is not very clear
Figure 3.5 (p. 108)
Stagnation points on bodies in flowing fluids.
Example 1. An airplane flies 100 mi/hr at an elevation of 10,000 ft in a standard atmosphere. Determine the pressure at point (1) far ahead of the airplane, the pressure at the stagnation point on the nose of the airplane (point 2)
Figure E3.6a (p. 110)
Figure E3.6b (p. 110)
Free Jets
Applying Bernoulli Equation between points (1) and (2),and using p 1 =0=p 2 ; z 1 =h; z 2 = 0, V 1 =0
V
2 2
V
2
h
2
gh
at point 2 ) at point 5
Figure 3.11 (p. 112)
Vertical flow from a tank.
An object falling a distance h from rest, velocity is given as:
Page 113
Use the centerline velocity as the average velocity as d< Figure 3.12 (p. 113) Horizontal flow from a tank. Vena contracta is because of the inability of the fluid to turn a sharp corner Figure 3.13 (p. 113) Vena contracta effect for a sharp-edged orifice. Figure 3.14 (p. 114) Typical flow patterns and contraction coefficients for various round exit configurations.