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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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Solution

The correct option is C Modulus of elasticity
Dimension of k must be same as pressure according to principle of dimensional homogeneity.
Thus it's dimensions are $M L^{- 1} T^{- 2}$ which is the same as modulus of elasticity (Stress/Strain).

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Similar questions

Q. 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

Q. 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 of

Q. 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

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Q. The hydrostatic pressure 'P' of a liquid column depends upon the density 'd' , height 'h' of liquid column and also an acceleration 'g; due to gravity. Using dimensional analysis, derive formula for pressure P.

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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 elasticityDimension of k must be same as pressure according to principle of dimensional homogeneity.Thus it's dimensions are ML−1T−2 which is the same as modulus of elasticity (Stress/Strain).

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
Dimension of k must be same as pressure according to principle of dimensional homogeneity.
Thus it's dimensions are $M L^{- 1} T^{- 2}$ which is the same as modulus of elasticity (Stress/Strain).