4.
A container filled with a liquid of density 4p as
shown in the figure. The velocity of efflux through
orifice is (p is density of water and g = 10 ms-2)
[NCERT Pg. 259]
Answers
Therefore the velocity of efflux through the orifice is 10 m/s.
Given:
The density of liquid = 4ρ
Acceleration due to gravity = g = 10 m/s²
Height from orifice to upper surface of liquid = h = 5 m
To Find:
The velocity of efflux through the orifice.
Solution:
We can simply solve this numerical problem by using the following process.
By Bernoulli's Energy Equation
P₁ + ρv₁²/2 + ρgh₁ = P₂ + ρv₂²/2 + ρgh₂
1 ⇒ point taken at the upper surface of the water.
Where P₁ = Atmospheric Pressure
v₁ = Velocity of the liquid = 0 m/s
2 ⇒ point taken at the orifice.
Where P₂ = Atmospheric Pressure
h₂ = height from efflux to efflux = 0
So the Bernouli's Energy equation becomes,
⇒ 0 + 0 + ρgh₁ = 0 + ρv₂²/2 + 0
⇒ gh₁ = v₂²/2
⇒ v₂ = √2gh₁
⇒ v₂ = √2 × 10 × 5
⇒ v₂ = √100
⇒ v₂ = 10 m/s
Therefore the velocity of efflux through the orifice is 10 m/s.
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