Question

Check the dimensional correctness of the following
Pressure P = ( ρgh )1/2
Where ρ is the density, g is the acceleration due to gravity, h is the height

Answer 1

Solution

According to given data

Pressure P = ( ρgh )1/2

Left hand side

$pressure=\frac{N}{m^2}= \frac{Kg - m}{m^2- sec^2}\\=\frac{Kg }{m-sec^2}$

Now Right hand side

$\rho gh=\frac{Kg }{m^3}.\frac{m }{sec^2}.m$

=$\frac{Kg }{m- sec^2}$

So left and right hand side are equal in dimensional.