E4.10 Pressure Drop, Unknown Pipe Diameter Case

Example 4.10: Water flows through a galvanized iron pipe at a rate of 0.085 ft³/s. Pressure drop is found to be 5 psi. Pipe is 105 feet long. Determine the size of the pipe. Use the following information:

Density of water = 62.36 lb/ft³; Viscosity of water = 7.56 ´ 10^-4 lb/(ft·s)

Roughness of the pipe = 0.0005 ft

Assume pipe is horizontal.

Solution

Frictional losses, h_f:

Assume friction factor f = 0.005

Diameter of the pipe, d (Equation 4.17)

Velocity of the fluid, V:

Reynolds number, Re (Equation 4.12):

Relative roughness, RR:

Revised friction factor, f_i+1 (Figure 4.3) = 0.0075.

Revised estimate of diameter (d_i+1) as

Revised velocity of water (V_i+1):

Revised Reynolds number (Re_i+1) as

Revised relative roughness (ε/d_i+1) = 0.0005/0.134 = 3.72 ´ 10^-3.

Friction factor, f_i+1 = 0.0074

Repeat these steps till convergence is achieved.

Next iteration gives diameter, d = 0.134 ft or 1.6 in.