Dimensional Analysis of Specific Speed: Explained

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  • Thread starter Thread starter Mikealvarado100
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    Specific Speed Unit
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Discussion Overview

The discussion focuses on the dimensional analysis of specific speed, defined by the formula Ns=N(Q^0.5)/(H^0.75). Participants explore the dimensional consistency of the formula and the implications of unit systems on its validity.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant presents the formula for specific speed and questions the dimensional analysis, noting that the dimensions of Q^0.5 do not seem to equal those of H^0.75.
  • Another participant requests clarification on the initial question posed.
  • A third participant urges for a dimensional analysis of the formula itself.
  • A later reply challenges the dimensionality of the formula, suggesting that it is only pseudo dimensionless and valid within a specific system of units, proposing that a proper dimensionless formula should include gravitational acceleration (g) in the denominator.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the dimensional analysis of specific speed, with differing views on the validity of the formula and the necessity of including additional factors like gravitational acceleration.

Contextual Notes

The discussion highlights potential limitations in the assumptions regarding unit systems and the definitions of the variables involved in the formula.

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.
 
Last edited:
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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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