EXAMPLE 5–8 Velocity Measurement by a Pitot Tube h3 = 12 cm A piezometer and a Pitot tube are tapped into a horizontal water pipe, as shown in Fig. 5-41, to measure static and stagnation (static + dynamic) pressures. For the indicated water column heights, determine the velocity at - the center of the pipe. h =7 cm h = 3 cm SOLUTION The static and stagnation pressures in a horizontal pipe are measured. The velocity at the center of the pipe is to be determined. Assumptions 1 The flow is steady and incompressible. 2 Points 1 and 2 are close enough together that the irreversible energy loss between these two points is negligible, and thus we can use the Bernoulli equation. Analysis We take points 1 and 2 along the centerline of the pipe, with point 1 directly under the piezometer and point 2 at the tip of the Pitot tube. This is a steady flow with straight and parallel streamlines, and the gage pres- sures at points 1 and 2 can be expressed as Water Stagnation point FIGURE 5-41 Schematic for Example 5–8. P, = pg(h, + h,) P2 = pg(h, + h, + h3)

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EXAMPLE 5-8
Velocity Measurement by a Pitot Tube
h = 12 cm
A piezometer and a Pitot tube are tapped into a horizontal water pipe, as
shown in Fig. 5-41, to measure static and stagnation (static + dynamic)
pressures. For the indicated water column heights, determine the velocity at
the center of the pipe.
h = 7 cm
h = 3 cm
SOLUTION The static and stagnation pressures in a horizontal pipe are
measured. The velocity at the center of the pipe is to be determined.
Assumptions 1 The flow is steady and incompressible. 2 Points 1 and 2 are
close enough together that the irreversible energy loss between these two
points is negligible, and thus we can use the Bernoulli equation.
Analysis We take points 1 and 2 along the centerline of the pipe, with point
1 directly under the piezometer and point 2 at the tip of the Pitot tube. This
is a steady flow with straight and parallel streamlines, and the gage pres-
sures at points 1 and 2 can be expressed as
Water
Stagnation
point
FIGURE 5-41
Schematic for Example 5–8.
P, = pg(h, + h,)
P2 = pg(h, + h, + h3)
Transcribed Image Text:EXAMPLE 5-8 Velocity Measurement by a Pitot Tube h = 12 cm A piezometer and a Pitot tube are tapped into a horizontal water pipe, as shown in Fig. 5-41, to measure static and stagnation (static + dynamic) pressures. For the indicated water column heights, determine the velocity at the center of the pipe. h = 7 cm h = 3 cm SOLUTION The static and stagnation pressures in a horizontal pipe are measured. The velocity at the center of the pipe is to be determined. Assumptions 1 The flow is steady and incompressible. 2 Points 1 and 2 are close enough together that the irreversible energy loss between these two points is negligible, and thus we can use the Bernoulli equation. Analysis We take points 1 and 2 along the centerline of the pipe, with point 1 directly under the piezometer and point 2 at the tip of the Pitot tube. This is a steady flow with straight and parallel streamlines, and the gage pres- sures at points 1 and 2 can be expressed as Water Stagnation point FIGURE 5-41 Schematic for Example 5–8. P, = pg(h, + h,) P2 = pg(h, + h, + h3)
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