Question

According to fire regulations in a town, the pressure drop in a commercial steel, horizontal pipe must not exceed 2.0 psi per 250 ft of pipe for flow rates up to 500 gal/min. If the water temperature is never below 50˚F, what diameter pipe is needed?

Answer 1

6.37 inch

Step-by-step explanation:

Thinking process:

We need to know the flow rate of the fluid through the cross sectional pipe. Let this rate be denoted by Q.

To determine the pressure drop in the pipe:

Using the Bernoulli equation for mass conservation:

`(P1)/(\rho ) + (v_(2) )/(2g) +z_(1) = (P2)/(\rho ) + (v2^(2) )/(2g) + z_(2) + f(l)/(D) (v^(2) )/(2g)`

thus

`(P1-P2)/(\rho ) = f(l)/(D) (v^(2) )/(2g)`

The largest pressure drop (P1-P2) will occur with the largest f, which occurs with the smallest Reynolds number, Re or the largest V.

Since the viscosity of the water increases with temperature decrease, we consider coldest case at T = 50⁰F

from the tables

Re= 2.01 × 10⁵

Hence, f = 0.018

Therefore, pressure drop, (P1-P2)/p = 2.70 ft

This occurs at ae presure change of 1.17 psi

Correlating with the chart, we find that the diameter will be D= 0.513

= 6.37 in Ans