Question

Water is supplied to a business in a 1.063-inch diameter copper pipe at 5 ft/s. Friction factor f = 0.025 for this pipe.

a. Find the pressure drop over 100 ft of this pipe. [Answer: 5 psia, which is significant considering that the water supply is usually about 50 psig. Bends in the pipe and other pipe fittings reduce the water pressure even more, of course.]

b. What is the volumetric flow rate of water gpm?

Answer 1

Solution

Given data:

WRITING ALL UNITS IN SI UNIT SYSTEM

Diameter of supply pipe D= 1.063 inch = 0.027m

Average Velocity of flow V = 5 ft/s = 1.52 m/s

Darcy-Weishback friction factor = 0.025

Length of pipe L =100 ft = 30.3m

Supply pressure = 50 psig

a) Pressure drop

We have the to find out the pressure loss from the realtion connecting head loss due to friction and pressure loss,

h_f = Delta P / density x g

h_f = f L V² / 2 gD

= 0.025 x 30.3 x1.52² / 2 x 9.81 x 0.027=3.303 m

Therefore Delta P pressure loss = h_f x density x g = 3.303 x 1000 x 9.81 = 32402.43 Pa

Converting Pascal to psia = 32402.43 /6895 = 4.699 psia

b)Volumetric flow rate of water,

Q = Area of crosection x Average velocity = PI / 4 D² x V = (22/7 x4) x 0.027² x 1.52 = 8.7 x 10^-4 m³ /s

Converting to gpm = 8.7 x 10^-4 x 15850.32314 = 13.79 gpm