If the piping between the inlet to your home at 60psig and a

If the piping between the inlet to your home (at 60psig) and a sink is made up of the pipe (e/D = 0.001) and fittings shown below estimate the flow rate for a single sink. 60 psig |------ 30ft of 1/4 \" pipe ----- 5x 90degree elbows ----- 90degree angled valve rightarrow sink (ambient)

Solution

Assume flowrate Q = 8 gal/min = 0.01782 ft³/s

Dia of pipe d = 1/4\" = 0.020833 ft

Cross-section area A = pi/4 * d² = 3.14 / 4 * 0.020833² = 3.41 *10^-4 ft²

Velocity V = Q / A

= 0.01782 / 3.41 *10^-4

= 52.27 ft/s

Reynolds number Re = V*d / neu

= 52.27 * 0.020833 / (1.08*10^-5)

= 100,000

From Moody diagram for Re = 100,000 and e/d = 0.001, we get frcition factor f = 0.0225

Loss coeff for pipe = fL/D = 0.0225*30 / 0.020833 = 32.4

For 90 deg elbows, loss coefficient K = 0.3

For fully open 90 deg angled valve, loss coeff K = 2

For exit from, sink, K = 1

Total K = 5*0.3 + 2 + 1 = 4.5

Sum of pipe loss + minor fittings = 32.4 + 4.5 = 36.9

We have Pressure drop = Loss*rho * V² / 2g

= 36.9 * 62.4 * 52.27² / (2*32.2)

= 97685.5 lb/ft²

= 97685.5 / 12² psig

= 678.4 psig

This is higher than the given value of 60 psig. Hence, we need to re-iterate by assuming a new value (probably lower) of Q.