In the subject of Fluid Mechanics, we will discover that the pressure of a fluid
ID: 1939431 • Letter: I
Question
In the subject of Fluid Mechanics, we will discover that the pressure of a fluid passing through a valve or other restriction in a pipeline will decrease abruptly. The amount of the pressure decrease. Delta P, is related to fluid density, p. and the fluid mean velocity, V. The form of the equation that predicts the amount of pressure drop is: Delta P = C*p*V degree where C and a are dimensionless constants. By comparing the dimensions of the variables involved in the equation, determine the value of the constant 'a'.Explanation / Answer
In the following [] denotes the dimension of . We know that
[P] = [ML-1T-2] [] = [ML-3] [V]=[LT-1] [C] = [1] = Dimensionless
Therefore
[ML-1T-2] =[1][ML-3][LT-1]a
or
[ML-1T-2]=[ML-3+aT-a]
Therefoore, a =2.