Dimensional Analysis of Specific Speed: Explained

[Mikealvarado100]

Hi
Specific Speed is defined as:
N_s=N(Q^0.5)/(H^.75)
How Dimensional Analysis of it can be done? Unit of N is 1/sec and N_{s is unitless. Then Dimension of Q^0.5 must be equal to dimension of H^0.75. It seems no to be equal.
Please explain it.}

 

[Nidum]

What is your question ?

 

[Mikealvarado100]

Please analyse the formula dimensionally.

 

[Nidum]

Your formula is only pseudo dimensionless . The calculated N_s number is only valid for a specific system of units .

The proper dimensionless formula has a g in the denominator . Explained reasonably well in Wikipedia .