Dimensional Analysis of Specific Speed: Explained

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Specific Speed (Ns) is defined as Ns = N(Q^0.5)/(H^0.75), where N is in 1/sec, and Ns is unitless. Dimensional analysis indicates that the dimensions of Q^0.5 and H^0.75 do not align, suggesting that the formula is not truly dimensionless. The discussion highlights that the calculated Ns value is only valid within a specific system of units. A proper dimensionless formulation should include gravitational acceleration (g) in the denominator. The Wikipedia explanation provides a clearer understanding of these dimensional considerations.
Mikealvarado100
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Hi
Specific Speed is defined as:
Ns=N(Q^0.5)/(H^.75)
How Dimensional Analysis of it can be done? Unit of N is 1/sec and Ns 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.
 
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What is your question ?
 
Please analyse the formula dimensionally.
 
Your formula is only pseudo dimensionless . The calculated Ns 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 .
 

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