question_answer

A hole is made at the bottom of the tank filled with water (density\[\text{1000}\,\text{kg/}{{\text{m}}^{\text{3}}}\]). If the total pressure at the bottom of the tank is 3 atmosphere (1 atmosphere\[\text{=1}{{\text{0}}^{\text{5}}}\,\text{N/}{{\text{m}}^{\text{2}}}\]), 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 Bernoullis theorem \[{{p}_{1}}+0+\rho gH={{p}_{2}}+\frac{1}{2}\rho {{v}^{2}}+\rho gH\] \[{{p}_{1}}-{{p}_{2}}=\frac{1}{2}\rho {{v}^{2}}\] \[3\times {{10}^{5}}-1\times {{10}^{5}}=\frac{1}{2}\rho {{v}^{2}}\] \[2\times {{10}^{5}}=\frac{1}{2}\rho {{v}^{2}}\] \[2\times {{10}^{5}}=\frac{1}{2}\times {{10}^{3}}\times {{v}^{2}}\] \[{{v}^{2}}=400\] \[v=\sqrt{400}\]