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Citrus2011 [14]

2 years ago

8

Water at 20°C flows by gravity through a smooth pipe from one reservoir to a lower one. The elevation difference is 60 m. The pi

pe is 360 m long, with a diameter of 12 cm. For the given system a pump is used at night to drive water back to the upper reservoir. If the pump delivers 15,000 W to the water, estimate the flow rate. For water at 20°C, take rho = 998 kg/m3 and μ = 0.001 kg/m-s. Round the answer to the nearest whole number.

1 answer:

Serga [27]2 years ago

7 0

Answer:

Flow Rate = 80 m^3 /hours (Rounded to the nearest whole number)

Explanation:

Given

Hf = head loss
f = friction factor
L = Length of the pipe = 360 m
V = Flow velocity, m/s
D = Pipe diameter = 0.12 m
g = Gravitational acceleration, m/s^2
Re = Reynolds's Number
rho = Density =998 kg/m^3
μ = Viscosity = 0.001 kg/m-s
Z = Elevation Difference = 60 m

Calculations

Moody friction loss in the pipe = Hf = (f*L*V^2)/(2*D*g)

The energy equation for this system will be,

Hp = Z + Hf

The other three equations to solve the above equations are:

Re = (rho*V*D)/ μ

Flow Rate, Q = V*(pi/4)*D^2

Power = 15000 W = rho*g*Q*Hp

1/f^0.5 = 2*log ((Re*f^0.5)/2.51)

We can iterate the 5 equations to find f and solve them to find the values of:

Re = 235000

f = 0.015

V = 1.97 m/s

And use them to find the flow rate,

Q = V*(pi/4)*D^2

Q = (1.97)*(pi/4)*(0.12)^2 = 0.022 m^3/s = 80 m^3 /hours

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The height of the water would be 29010.53917 m

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