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Standard XII

Physics

Dimensional Analysis

The Bernoulli...

Question

The Bernoulli's equation is given by $P + \frac{1}{2} ρ v^{2} + h ρ g = k$ .
Where, $P =$ pressure
$ρ =$ density
$v =$ speed
$h =$ height of the liquid column
$g =$ acceleration due to gravity, and
$k$ is constant.
The dimensional formula for $k$ is same as that for

velocity gradient

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pressure gradient

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modulus of elasticity

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thrust

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Solution

The correct option is C modulus of elasticity
$[k] = [ρ] [v^{2}] = [M L^{- 3}] [L^{2} T^{- 2}] = M L^{- 1} T^{- 2}$
$= \frac{F o r c e}{A r e a} = M o d u l u s o f e l a s t i c i t y$

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where

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The Bernoulli's equation is given by P+12ρv2+hρg=k. Where, P= pressure ρ= density v= speed h= height of the liquid column g= acceleration due to gravity, and k is constant. The dimensional formula for k is same as that for

The correct option is C modulus of elasticity[k]=[ρ][v2]=[ML−3][L2T−2]=ML−1T−2=ForceArea=Modulusofelasticity

The Bernoulli's equation is given by $P + \frac{1}{2} ρ v^{2} + h ρ g = k$ .
Where, $P =$ pressure
$ρ =$ density
$v =$ speed
$h =$ height of the liquid column
$g =$ acceleration due to gravity, and
$k$ is constant.
The dimensional formula for $k$ is same as that for

The correct option is C modulus of elasticity
$[k] = [ρ] [v^{2}] = [M L^{- 3}] [L^{2} T^{- 2}] = M L^{- 1} T^{- 2}$
$= \frac{F o r c e}{A r e a} = M o d u l u s o f e l a s t i c i t y$