Respuesta :
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, [tex]head\ loss = \frac{f L V^2}{( 2 g D)}[/tex]
where, f = Darcy friction factor
V = flow velocity
g = acceleration due to gravity
We know, flow rate Q = A x V
solving for V
[tex]V = \frac{Q}{A}[/tex]
[tex]= \frac{0.16}{\frac{\pi}{4} (0.318)^2} = 2.015 m/s[/tex]
obtained Darcy friction factor
calculate Reynold number (Re) ,
[tex]Re = \frac{\rho V D}{\mu}[/tex]
where,[tex]\rho[/tex] = density of water
[tex]\mu[/tex] = Dynamic viscosity of water at 15 degree C = 0.001 Ns/m2
so reynold number is
[tex]Re = \frac{1000\times 2.015\times 0.318}{0.001}[/tex]
= 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
[tex]HL = \frac{0.0126 (200)(2.015)^2}{( 2 \times 9.81 \times 0.318)}[/tex]
HL = 1.64 m
