First slide

Fluid dynamics

Question

There is a hole in the bottom of tank having water. If total pressure at bottom is 3 atm (1 atm = 10⁵N/m²) then the velocity of water flowing from hole is

Moderate

A

$\sqrt{400} m / s$
B

$\sqrt{600} m / s$
C

$\sqrt{60} m / s$
D

None of these

Solution

Pressure at the bottom of tank $P = 3 \times 10^{5} \frac{N}{m^{2}}$
Pressure due to liquid column
P_l = $ρgh = 3 \times 10^{5} - 1 \times 10^{5} = 2 \times 10^{5}$ N/m²
and velocity of water $v = \sqrt{2 gh}$
$∴ v = \sqrt{\frac{2 P_{l}}{ρ}} = \sqrt{\frac{2 \times 2 \times 10^{5}}{10^{3}}} = \sqrt{400} m / s$

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