Question

In the figure, water flows through a horizontal pipe and then out into the atmosphere at a speed v_1 = 14.0 m/s. The diameters of the left and right sections of the pipe are 5.20 cm and 2.90 cm. (a) What volume of water flows into the atmosphere during a 10 min period? In the left section of the pipe, what are (b) the speed v_2 and (c) the gauge pressure?

Answer 1

(a) Rate of flow

$Q=AV = \frac{\Pi d_{1}^{2}}{4}V_{1}=\frac{\Pi \times (5.2\times 10^{-2})^{2}}{4}\times 14=0.0297 m^{3}/s$

in 10 minutes

$Volume = Q\times 10\times 60=0.0297\times 10\times 60 =17.82 m^{3}$

(b) Also

$Q=A_{2}V_{2} = \frac{\Pi d_{1}^{2}}{4}V_{2}=\frac{\Pi \times (2.9\times 10^{-2})^{2}}{4}\times V_{2}=0.0297 m^{3}/s$

Bernulli's Principle

$\frac{P1}{\rho g}+\frac{V_{1}^{2}}{2g}+h = \frac{P_{2}}{\rho g}+\frac{V_{2}^{2}}{2g}+h$

$P_{1}-P_{2}=\frac{V_{2}^{2}-V_{1}^{2}}{2}\rho =\frac{44.965^{2}-14^{2}}{2}\times 1000=9.13\times 10^{5}pa$