Question

A hole is made at the bottom of the tank filled with water (density =1000 kgm^(-3)). If the total pressure at the bottom of the tank is three atmospheres (1 atmosphere =10^(5) Nm^(-2)), then the velocity of efflux is nearest to

Answer 1

$\bf{Given}\begin{cases}\sf{density,\rho=1000\:kgm^{-3}}\\ \ \sf{Pressure,P=3atm=3×10^{5}\:Nm^{-2}}\\ \ \sf{Atmospheric\: pressure,P_{0}=10^{5}Nm^{-2}}\end{cases}$

Now pressure due to liquid column is

$\longrightarrow\sf{P-P_{0}=\rho\:gh}$

Now, velocity of efflux is ;

$\longrightarrow\sf{v=\sqrt{2gh}}$

$\longrightarrow\sf{v=\sqrt{\frac{2(P-P_{0})}{\rho}}}$

$\longrightarrow\sf{v=\sqrt{\frac{2\times 3\times 10^{5}-10^{5}}{1000}}}$

$\longrightarrow\sf{v=20\:m^{-1}}$

•°• The velocity of efflux is 20 m/s.

Concept:—

The above question is based on Torricelli's Theorem which states that velocity of efflux from an orifice is equal to the velocity of free fall from surface to orifice. Given by the formula

→ v = √2gh

Answer 2

Answer:

Now pressure due to liquid column is

\longrightarrow\sf{P-P_{0}=\rho\:gh}⟶P−P

0

=ρgh

Now, velocity of efflux is ;

\longrightarrow\sf{v=\sqrt{2gh}}⟶v=

2gh

\longrightarrow\sf{v=\sqrt{\frac{2(P-P_{0})}{\rho}}}⟶v=

ρ

2(P−P

0

)

\longrightarrow\sf{v=\sqrt{\frac{2\times 3\times 10^{5}-10^{5}}{1000}}}⟶v=

1000

2×3×10

5

−10

5

\longrightarrow\sf{v=20\:m^{-1}}⟶v=20m

−1

•°• The velocity of efflux is 20 m/s.

Concept:—

The above question is based on Torricelli's Theorem which states that velocity of efflux from an orifice is equal to the velocity of free fall from surface to orifice. Given by the formula

→ v = √2gh

Explanation:

hope its help you......

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