Bernoulli's equation is given by p +frac{1}{2} ρ v ^{2}+ h ρ g = k where p = pressure, ρ = de

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1.Units, Dimensions and Measurement

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The Bernoulli's equation is given by $p +\frac{1}{2} \rho v ^{2}+ h \rho g = k$

where $p =$ pressure, $\rho =$ 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

A

Velocity gradient

B

Pressure gradient

C

Modulus of elasticity

D

Thrust

Solution

$[ k ]=[\rho]\left[ v ^{2}\right]=\left[ ML ^{-3}\right]\left[ L ^{2} T ^{-2}\right]= ML ^{-1} T ^{-2}$

$=\frac{\text { Force }}{\text { Area }}=$ Modulus of elasticity

Standard 11

Physics

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