| Water flows in a horizontal tube (see figure). The pressure of water changes by 700 \[N{{m}^{2}}\] between A and B where the area of cross section are 40 \[c{{m}^{2}}\]and 20\[c{{m}^{2}}\], respectively. Find the rate of flow of water through the tube. |
| (density of water = 1000\[kg{{m}^{3}}\]) |
 |
A) \[3020c{{m}^{3}}/s\]
B) \[1810c{{m}^{3}}/s\]
C) \[2720c{{m}^{3}}/s\]
D) \[2420c{{m}^{3}}/s\]
Correct Answer: C
Solution :
| [c] \[\left( {{P}_{A}}-{{P}_{B}} \right)=\frac{1}{2}\rho \left( V_{B}^{2}-V_{A}^{2} \right)\] |
| \[\Rightarrow \Delta P=\frac{1}{2}\rho \left( V_{B}^{2}-\frac{V_{B}^{2}}{4} \right)\] |
| \[\Rightarrow \Delta P=\frac{3}{8}\rho V_{B}^{2}\] |
| \[{{V}_{B}}=\sqrt{\frac{\left( \Delta P \right)8}{3\rho }}=\sqrt{\frac{\left( \Delta P \right)4}{1500}}=\sqrt{\frac{700\times 4}{1500}}m/s\] |
| \[Q={{A}_{B}}{{V}_{B}}=\left( 20 \right)\left( \sqrt{\frac{28}{15}} \right)\times 100\frac{c{{m}^{3}}}{s}\] |
| \[Q\approx 2720c{{m}^{3}}/s\] |
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