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where, coefficient 4 and 1/2 aredimensionless constants, f =dimensionless g = gr

ID: 1760805 • Letter: W

Question

where, coefficient 4 and 1/2 aredimensionless constants,

f =dimensionless                            g = gravitional acceleration, ft/s2

= density, lbm /ft3                                  L= length, ft

v = velocity,ft/s                              D = diameter, ft

performing a dimensional analysis onthe equation, explain in detail why you agree or disagree with thewriter.

Explanation / Answer

L/D is ft/ft => dimensionless v2/2g is ft2s-2s2/ft => ft   is lbm/ft3 so *v2/2g*L/D = lbm/ft2 => mass/area But the left side has units of pressure => force/area recall that mass*acceleration = force. It is missing another termwith units of acceleration. So the equation is dimensionally inconsistent.

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