A 75-mm diameter pipe is reduced to a 50-mm diameter pipe as shown in Figure 3.5

Question

A 75-mm diameter pipe is reduced to a 50-mm diameter pipe as shown in Figure 3.53. A static tube is installed in the 75-mm pipe and a Pitot tube is installed in the 75-mm pipe. Determine the difference, h, between the water levels in the static tube and the Pitot tube when the flow rate in the pipe is 10 L/s. How would h be different if a lighter (i.e., less dense) liquid were used instead of water; the same volumetric flow rate in both cases.

A 75-mm diameter pipe is reduced to a 50-mm diameter pipe as shown in Figure 3.53. A static tube is installed in the 75-mm pipe and a Pitot tube is installed in the 75-mm pipe. Determine the difference, delta h, between the water levels in the static tube and the Pitot tube when the flow rate in the pipe is 10 L/s. How would delta h be different if a lighter (i.e., less dense) liquid were used instead of water; the same volumetric flow rate in both cases.

Explanation / Answer

Area A1 = pi/4 * 75^2 = 4415.625 mm^2 = 0.004415625 m^2

Area A2 = pi/4 *50^2 = 1962.5 mm^2 = 0.0019625 m^2

Flowrate Q = 10 L/s = 0.01 m^3/s

Velocity V1 = Q/A1 = 0.01 / 0.004415625 = 2.265 m/s

Velocity V2 = Q/A2 = 0.01 / 0.0019625 = 5.096 m/s

Static tube measures static pressure while pitottube measures total pressure.

P1 + 1/2*rho*V1^2 = P2 + 1/2*rho*V2^2 = Pt

Pt - P1 = 1/2*rho*V1^2

rho*g*h = 1/2*rho*V1^2

h = V1^2 / (2g).............1

h = 2.265^2 / (2*9.81)

h = 0.2615 m = 261.5 mm

As seen from eqn 1, h is independent of density of fluid.

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