Answer:
[tex]\frac{\delta p }{l} = 30.4 lb/ft^3[/tex]
Explanation:
Given data:
flow rate = 10 gallon per minute = 0.0223 ft^3/sec
diameter = 0.75 inch
we know discharge is given as
Q = VA
solve for velocity V = \frac{Q}{A}[/tex]
[tex] V = \frac{0.223}{\frac{\pi}{4} \frac{0.75}{12}}[/tex]
V = 7.27 ft/sec
we know that Reynold number
[tex]Re = \frac{VD}{\nu}[/tex]
[tex]Re = \frac{7.27 \times \frac{0.75}{12}}{1.21\times 10^{-5}}[/tex]
[tex]Re = 3.76 \times 10^4 [/tex]
calculate the [tex]\frac{\epsilon }{D} [/tex]ratio to determine the fanning friction f
[tex]\frac{\epsilon }{D} = \frac{0.0005}{\frac{0.75}{12}} = 0.008[/tex]
from moody diagram f value corresonding to Re and [tex]\frac{\epsilon }{D} [/tex]is 0.037
for horizontal pipe
[tex]\delta p = \frac{f l \rho v^2}{2D}[/tex]
[tex]\frac{\delta p }{l} = \frac{1 \times 0.037 \times 1.94 \times 7.27}{\frac{0.75}{12}}[/tex]
where 1.94 slug/ft^3is density of water
[tex]\frac{\delta p }{l} = 30.4 lb/ft^3[/tex]
