Respuesta :
Explanation:
The given data is as follows.
[tex]P_{1}[/tex] = 85 psig, [tex]P_{2}[/tex] = [tex]P_{atm}[/tex] = 15 psia
Q = 1620 gpm, d = 2.5 inch, l = 8 ft = 2.4384 m
According to Darey-Weisbach equation,
[tex]h_{l} = \frac{4fl \nu^{2}}{2gD}[/tex] ......... (1)
Value of 'f' will be decided on the basis of Reynold number.
As, it is known that [tex]R_{l} = \frac{\rho \nu d}{\mu}[/tex]
where, [tex]\mu_{water}[/tex] = [tex]10^{-3}[/tex] kg/ms
As it is known that 1 gpm = [tex]\frac{1}{3.67} m^{3}/hr[/tex]
So, [tex]1 m^{3}/hr[/tex] = 3.67 gpm
Therefore, Q = [tex]1620 \times \frac{1}{3.67}[/tex]
= [tex]441.4168 m^{3}/hr[/tex]
= 0.1226 [tex]m^{3}/s[/tex]
In, 1 inch = 2.54 cm = 0.0254 m
Therefore, d = 2.5 \times 0.0254 = 0.0635 m
V = [tex]\frac{Q}{\frac{\pi}{4}d^{2}}[/tex]
= [tex]\frac{0.1226}{0.785 \times (0.0635)^{2}}[/tex]
= 38.73 m/s
Hence, we will calculate Reynold number as follows.
[tex]R_{l}[/tex] = [tex]\frac{1000 \times 38.73 \times 0.0635}{10^{-3}}[/tex]
= 2459355
As [tex]R_{l}[/tex] > 2000 then, it means that flow is turbulent.
As, f = 0.079 [tex]R^{-0.25}_{l}[/tex]
= 0.001994
Putting all the values into equation (1) formula as follows.
[tex]h_{l} = \frac{4fl \nu^{2}}{2gD}[/tex]
= [tex]\frac{4 \times 0.001994 \times 2.4384 \times (38.73)^{2}}{2 \times 9.81 \times 0.0635}[/tex]
= [tex]1.04069 \times 10^{5} m[/tex]
Thus, we can conclude that friction loss from the main to the discharge point is [tex]1.04069 \times 10^{5} m[/tex].
