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  • In the diagram shown, the difference in the two tubes of the manometer is 5 cm, the cross section of the

In the diagram shown, the difference in the two tubes of the manometer is 5 cm, the cross section of the tube at A and B is 6 mm2 and 10 mm2 respectively. The rate at which water flows through the tube is (g=10 ms-2)

 

Option: 1

7.5 cc/s


Option: 2

8.0 cc/s


Option: 3

10.0 cc/s


Option: 4

12.5 cc/s


Answers (1)

best_answer

\\ Let \ the \ velocities \ at \ the \ ends\ A \ and \ B \ be \ v_{1} \ and \ v_{2} \\ \\ Using, \ \text{equation of continuity} \ \ 6 v_{1}=10 v_{2} \Rightarrow v_{1}=\frac{5}{3} v_{2}\\ \\ Now, \ \text{using Bernoulli's equation}: \\ \\ P_{1}+\frac{1}{2} \rho v_{1}^{2}=P_{2}+\frac{1}{2} \rho v_{2}^{2} P_{1}-P_{2}=\frac{1}{2} \rho\left(\frac{16}{9} v_{2}^{2}\right) \\ \\ 0.05 \rho g=\frac{1}{2} \rho\left(\frac{16}{9} v_{2}^{2}\right) \\ Hence, v_{2}=0.75 m / s =75 cm / s \\ \\ Hence, \ \text{the total flow rate} =A v=75 \times 10^{-1} cm ^{3} / s =7.5 cc / s

 

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Ritika Jonwal

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