Answer:
Head loss is 1.64
Explanation:
Given data:
Length (L) = 200 m
Discharge (Q) = 0.16 m3/s
According to table of nominal pipe size , for schedule 80 , NPS 14, pipe has diameter (D)= 12.5 in or 31.8 cm 0.318 m
We know, ![head\ loss = \frac{f L V^2}{( 2 g D)}](https://tex.z-dn.net/?f=head%5C%20loss%20%20%3D%20%5Cfrac%7Bf%20L%20V%5E2%7D%7B%28%202%20g%20D%29%7D)
where, f = Darcy friction factor
V = flow velocity
g = acceleration due to gravity
We know, flow rate Q = A x V
solving for V
![V = \frac{Q}{A}](https://tex.z-dn.net/?f=V%20%3D%20%5Cfrac%7BQ%7D%7BA%7D)
![= \frac{0.16}{\frac{\pi}{4} (0.318)^2} = 2.015 m/s](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B0.16%7D%7B%5Cfrac%7B%5Cpi%7D%7B4%7D%20%280.318%29%5E2%7D%20%3D%202.015%20m%2Fs)
obtained Darcy friction factor
calculate Reynold number (Re) ,
![Re = \frac{\rho V D}{\mu}](https://tex.z-dn.net/?f=Re%20%3D%20%5Cfrac%7B%5Crho%20V%20D%7D%7B%5Cmu%7D)
where,
= density of water
= Dynamic viscosity of water at 15 degree C = 0.001 Ns/m2
so reynold number is
![Re = \frac{1000\times 2.015\times 0.318}{0.001}](https://tex.z-dn.net/?f=Re%20%3D%20%5Cfrac%7B1000%5Ctimes%202.015%5Ctimes%200.318%7D%7B0.001%7D)
= 6.4 x 10^5
For Schedule 80 PVC pipes , roughness (e) is 0.0015 mm
Relative roughness (e/D) = 0.0015 / 318 = 0.00005
from Moody diagram, for Re = 640000 and e/D = 0.00005 , Darcy friction factor , f = 0.0126
Therefore head loss is
![HL = \frac{0.0126 (200)(2.015)^2}{( 2 \times 9.81 \times 0.318)}](https://tex.z-dn.net/?f=HL%20%3D%20%5Cfrac%7B0.0126%20%28200%29%282.015%29%5E2%7D%7B%28%202%20%5Ctimes%209.81%20%5Ctimes%200.318%29%7D)
HL = 1.64 m