Problem 4.1.1

Water is passing through 4-in ID pipe. A manometer connected to the pitot tube measures a pressure drop of one inch of mercury. What is the flow rate of water?

Solution:

For manometers, pressure drop (delta P) is directly related to delta h. If manometer fluid density is rho_m then, delta P is equal to delta h times rho_m minus rho times g over gc. If height is measured in feet, density in pounds per cubic foot, then delta P values is in pound-force per foot squared.

Specific gravity of mercury is 13.59. Density of water at 110 degrees Fahrenheit is 61.86 pounds per cubic foot. Density of mercury can be calculated as 840.68 pounds per cubic foot. Pressure drop is calculated as 64.9 pounds per square foot (psf).

Velocity of the fluid passing though the pipe is given by C time square root of 2 gc delta P over rho, where C is the ‘Pitot Tube Constant” and is given as one. Rho is the density of the fluid (water) that is passing though pipe. Velocity is calculated as 8.217 foot per second.

Volumetric flow rate, q, can be obtained by multiplying velocity with cross-sectional area (A). For a 4-in ID-pipe, flow-area is 0.088 square foot. Water flow rate is 0.726 cubic foot per second.