A) The volume of the liquid flowing through the tube in unit time is \[{{A}_{1}}{{v}_{1}}\]
B) \[{{v}_{2}}-{{v}_{1}}=\sqrt{2gh}\]
C) \[v_{2}^{2}-v_{1}^{2}=2gh\]
D) The energy per unit mass of the liquid is the same in both sections of the tube
Correct Answer: C
Solution :
According to Bernoulli's theorem, \[{{P}_{1}}+\frac{1}{2}\rho v_{1}^{2}={{P}_{2}}+\frac{1}{2}\rho v_{2}^{2}\] Þ \[{{P}_{1}}-{{P}_{2}}=\frac{1}{2}\rho \left( v_{2}^{2}-v_{1}^{2} \right)\]Þ \[h\rho g=\frac{1}{2}\rho \left( v_{2}^{2}-v_{1}^{2} \right)\] \ \[v_{2}^{2}-v_{1}^{2}=2gh\] Hence option (c) is correct.
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