Question

Water at a pressure of 3.3 atm at street level flows into an office building at a speed of 0.50 m/s through a pipe 5.0 cm in diameter. The pipe tapers down to 2.5 cm diameter by the top floor, 25 m above. Calculate the flow velocity and pressure in this pipe on the top floor.

Answer 1

Answer:

The flow velocity at the top is 2 m/s and the pressure at the top is 0.78 atm

Explanation:

As we know by equation of continuity

$A_1 v_1 = A_2v_2$

here we have

$A_1 = \frac{\pi}{4} d_1^2$

$A_2 = \frac{\pi}{4} d_2^2$

now we have

$\frac{\pi}{4} 5^2(0.50) = \frac{\pi}{4} (2.5)^2 v_2$

$v_2 = 2 m/s$

Now by Bernuolli's Theorem we have

$P_1 + \rho g h_1 + \frac{1}{2}\rho v_1^2 = P_2 + \rho g h_2 + \frac{1}{2}\rho v_2^2$

$3.3 \times 10^5 + (10^3)(10)(0) + \frac{1}{2}(1000)(0.50^2) = P_2 + (10^3)(10)(25) + \frac{1}{2}(10^3)(2^2)$

$3.3 \times 10^5 + 125 = P_2 + 2.5 \times 10^5 + 2000$

$P_2 = 0.78 atm$

#Learn

Topic : Bernuolli's Theorem

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