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MissTica
4 years ago
7

In rural areas, water is often extracted from underground by pumps. Consider an underground water source whose free surface is 6

0 m below ground level. The water is to be raised 5 m above the ground by a pump. The diameter of the pipe is 10 cm at the inlet and 15 cm at the exit. Neglecting any heat interaction with the surroundings and frictional heating effects, determine the power input to the pump required for a steady flow of water at a rate of 15 L/s (=0.015 m3/s)
Physics
1 answer:
stealth61 [152]4 years ago
6 0

Answer:

W = 9533.09 Watt

Explanation:

given,

diameter of pipe inlet, d₁ = 10 cm

                                      r₁ = 5 cm

diameter of pipe outlet, d₂ = 15 cm

                                      r₂= 7.5 cm

head upto water level is to rise = 60 + 5

                                          = 65 m

flow rate = 0.015 m³/s

we know

A₁ v₁ = A₂ v₂ = Q  

 π r₁² v₁ = π r₂² v₂  = 0.015

 v_1= \dfrac{r_2^2}{r_1^2} v_2

 v_1= \dfrac{7.5^2}{5^2} v_2

 v_1= 2.25 v_2

 v_2 = \dfrac{0.015}{\pi r_2^2}

 v_2 = \dfrac{0.015}{\pi 0.075^2}

    v₂ = 0.848 m/s

    v₁ = 1.908 m/s

Applying Bernoulli's equation

 P_p = \dfrac{1}{2}\rho (v_2^2-v_1^2)+ \rho g h

 P_p= \dfrac{1}{2}\times 1000\times (0.848^2-1.908^2)+ 1000\times 9.8\times 65

 P_p= 635539.32 Pa

 P_p is the pump pressure

Power of the pump

W = P_p x Q

W = 635539.32 x 0.015

W = 9533.09 Watt

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