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:


ANSWER

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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