Q.3 Consider the the following equation: Delta P = 14LV mu/D^2 where Delta P = P

Question

Q.3 Consider the the following equation: Delta P = 14LV mu/D^2 where Delta P = Pressure drop, lbf/ft^2 L = Pipe length, ft. V = Fluid velocity, ft/s. Mu = Fluid viscosity, lbm/(ft. s) D = Pipe diameter, ft. a. Is the equation dimensionally homogeneous? If so, are the units consistent? If not, what factor must be added to the right hand side of the equation to provide consistency? b. Convert the above equation so that all variables arc expressed in SI units and find out the value of the new constant. (Note: SI unit of pressure is Pa)

Explanation / Answer

a) The equation is not homogenous and not consistent.

Right side Numerator component = ft*ft*lb

Denominator = sec*ft*ft*ft*sec

So Numerator/Denominator = lb/(ft*sec^2)

Left side unit = (lb*ft)/(ft*ft*sec*sec) {Convert the force unit to mass*acceleration unit} = lb/ft*sec^2

So for Left side = Right side without any such conversion divide the right side with acceleration unit (ft/sec^2). (This is the factor)

b) In SI units:

Pressure = Pascal = Newton/metre^2 = kilogram*metre/metre^2*sec^2

Unit of factor in SI = metre/sec^2

Other components units:

Length = metre

Pipe diameter = metre

Fluid Velocity = metre/sec

Fluid Viscosity = kilogram/metre*sec

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