Respuesta :
Answer:
P = 24.38 hp
Explanation:
Given data:
diameter of steel pipe = 3 inc
length of pipe = 2001 ft
elevation of pond = 4286 ft
elevation of snow making machine = 4620 ft
Rate of water = 0.26 ft^3/s
Applying bernouli equation on bioth side
[tex]\frac{P}{\rho} + \frac{v_1^2}{2g} + z_1 + h_p =\frac{P_2}{\rho} + \frac{v_2^2}{2g} + z_2 + \frac{flv^2}{2gD} [/tex].....1
where P_2 = 182 psi
P_1 = 0, v_1 = 0
[tex]V =V_2 = \frac{Q}{\frac{\pi}{4} D^2}= \frac{0.26}{\frac{\pi}{4} \times (3/12)^2} = 5.30 ft/s[/tex]
calculation fro friction factor
from standard table we have
[tex]\frac{\epsilon}{D} = \frac{0.00015}{(3/12)} = 6\times 10^{-4}[/tex]
[tex]Re =\frac{VD}[\nu} = \frac{5.30 \times (3/12)}{1.66 \times 10^{-5}} = 7.96 \times 10^4 [/tex]
so for calculated R and[tex] \frac{\epsilon}{D}[/tex], F value = 0.0212
from equation 1
[tex]h_p = \frac{P_2}{\rho} + Z_2 -Z_1 +(1 + f\frac{l}{D}) \frac{V^2}{2g}[/tex]
[tex]h_p = \frac{182 \times 144/ lb /ft^2}{62.4} + 4620 - 4286 + (1 + 0.0212 \frac{2001}{(3/12)}) \frac{5.30}{2\times 32.2}[/tex]
h_p = 826.76ft so that
[tex]P = \rho Q h_p = 62.4 \times 0.26 \times 826.76 = 13413.38 ft lb/s = 24.38 hp[/tex]
