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Euler’s Model Law

The law in which models are based on the Euler’s number is called as Euler’s model law.

Whenever pressure, forces are predominant as compare to other forces for dynamic similarity. the Euler’s number in the model must be equal to Euler’s number in the prototype.

Em = Ep

Vm /  √ Pm / ρm = Vp / √ Pp / ρp

If the fluid is same in model and prototype, then

ρm = ρp

Vm /  √ Pm  =  Vp / √ Pp

Euler’s law is applicable in following cases

(i)    Water hammer phenomenon
(ii)    Phenomenon of cavitations
(iii)    Fully turbulent flow in case closed pipe
(iv)    Models of aerofoil’s fan blades.
(v)    Pressure distribution on ship.

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