Problem 4.5.1:

Water flows through a pipe that has inside diameter of 2.067 inches and has a roughness of 0.0015 foot. Pipe is 100-foot long. If water is flowing at 5 feet per second, then estimate pressure drop through the pipe. Density of water is given as 62.3 pounds per cubic foot and viscosity is 2.37 pound per foot per hour.

Solution: For given situation, Z₁ = Z₂ = 0. (Points are at same elevation).

V₁ = V₂ (Points are within the pipe having constant diameter).

Pump work, w_p, = 0

Reynolds number is 8.15 times 10⁴. Relative roughness, epsilon over d, is 0.0087. Using Figure 4-14, friction factor can be read as 0.0079.

Skin friction losses, h_fs, are calculated as 5.02 foot pound-force per pound-mass. The Bernoulli’s equation reduces to P₁ over rho is equal to P₂ over rho plus h_f, where h_f is form friction loss. Bernoulli’s equation for this situation, gives, pressure drop of 312.75 psf or 2.17 psi.