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Physics Question on mechanical properties of fluid

A tank is filled with water. There is a hole in . the bottom. At the bottom total pressure is 3 atm3\, atm, then, the velocity of water flowing from h (1atm =105 N/m2)\left( \text{1atm }=\text{1}{{0}^{5}}\text{ N}/{{\text{m}}^{\text{2}}} \right) ,then, the velocity of water flowing from hole is

A

10m/s

B

20m/s

C

15m/s

D

25m/s

Answer

20m/s

Explanation

Solution

At bottom of tank
ρ=hρg=3×105N/m2 \rho= h \rho g =3 \times 10^{5} N / m ^{2}
Pressure due to liquid column
ρ1=3×105−1×105=2×105 \rho_{1}=3 \times 10^{5}-1 \times 10^{5}=2 \times 10^{5}
Velocity of water v=2ghv =\sqrt{2 gh }
v=2ρ1ρ=2×2×105103 =20m/s \begin{array}{l} v =\sqrt{\frac{2 \rho_{1}}{\rho}}=\sqrt{\frac{2 \times 2 \times 10^{5}}{10^{3}}} \\\ =20 m / s \end{array}