Physics

# Dimensional analysis of the equation ${ \left( Velocity \right) }^{ x }={ \left( Pressure \ difference \right) }^{ \frac { 3 }{ 2 } }.{ \left( density \right) }^{ \frac { -3 }{ 2 } }$ gives the value of $x$ as:

3

##### SOLUTION
$\displaystyle (Velocity)^{x}=(\Delta p)^\frac{3}{2} \ (d)^\frac{-3}{2}$
$(LT^{-1})^{x}=(M^{1}L^{-1}T^{-2})^{\frac{3}{2}}(MC^{3})^{\frac{-3}{2}}$
$M^{0}L^{x}T^{-x}=M^{0}L^{\frac{-3}{2}+\frac{9}{2}}T^{-3}$
$\Rightarrow x=3$

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Single Correct Medium Published on 18th 08, 2020
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