question_answer

A hole is made at the bottom of the tank filled with water (density\[1000kg/{{m}^{3}})\]. If the total pressure at the bottom of the tank is \[3\] atmosphere (1 atmosphere\[=105N/{{m}^{2}})\], then the velocity of efflux is

A) \[\sqrt{200}m/s\]                           

B) \[\sqrt{400}m/s\]

C) \[\sqrt{500}m/s\]                           

D)  \[\sqrt{800}m/s\]

Correct Answer: B

Solution :

Applying Bernoulli's theorem                 \[{{p}_{1}}+0+\rho ghH={{p}_{2}}+\frac{1}{2}\rho {{v}^{2}}+\rho gH\]                 \[{{p}_{1}}-{{p}_{2}}=\frac{1}{2}\rho {{v}^{2}}\]                 \[3\times {{10}^{5}}-1\times {{10}^{5}}=\frac{1}{2}\rho {{v}^{2}}\]                 \[2\times {{10}^{5}}=\frac{1}{2}\rho {{v}^{2}}\]                 \[2\times {{10}^{5}}=\frac{1}{2}\times {{10}^{3}}\times {{v}^{2}}\]                 \[{{v}^{2}}=400\]                 \[v=\sqrt{400}\]