Problem 4.5.2:

Calculate pipe length if pressure drop through an asphalted cast iron pipe (6.605 inches ID) is 20 psi, when water is flowing at 10 feet per second at 90 degrees Fahrenheit. Pipe roughness is 0.0004 foot. Density is 62.12 pounds per cubic foot and viscosity is 1.85 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. 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. h_f is calculated as 46.36 foot pound-force per pound-mass. With no fitting losses, h_fs is the same as h_f.

Reynolds number can be calculated as 6.654 times 10⁵. For the given relative roughness, epsilon over d, is 0.00073. Using Figure 4-14, friction factor can be read as 0.0047.

h_fs is given by 4 fL/D V² /2g_c. From this relationship, we can find pipe length as 875 ft.