Answer to Question #124507 in Classical Mechanics for nicomed mhina

Question

a jet of water of cross sectional area A and velocity V strikes normally on a stationery flat plates.the mass per unit volume of water is Q by dimensional analysis show that an expression for the force exerted by the jet against the plate is given by KAVQ

Answer 1

The dimension of force is $[F] = \text{MLT}^{-2}$.

We have:

Area A, L²

Velocity v, LT^-1

Mass per unit volume (density) Q, ML^-3

Since the force is proportional to the product of all these quantities in some power, i.e.,

$$F\propto A^av^bQ^c,$$

write

$$\text{MLT}^{-2}=(\text{L}^{2a})(\text{L}^b\text{T}^{-b})(\text{M}^c\text{L}^{-3c}),\\ \text{MLT}^{-2}=\text{L}^{2a+b-3c}\text{M}^{c}\text{T}^{-b},\\ c=1,\\ b=2,\\ a=1.$$

Thus,

$$F\propto Av^2Q,\\\text{or}\\ F=kAv^2Q.$$