Question

Ajet of water of cross section area
A and velocity 'v'inpinges nomally
on a stationary feat plate. The mass per
unit of volume of water is rho. by
dimensional analysis determine an
experesion for the force F exerted by
the jet against the plate?
- ​

Answer 1

Answer:

The dimension of force is [F] = \text{MLT}^{-2}[F]=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,F∝A

a

v

b

Q

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.MLT

−2

=(L

2a

)(L

b

T

−b

)(M

c

L

−3c

),

MLT

−2

=L

2a+b−3c

M

c

T

−b

,

c=1,

b=2,

a=1.

Thus,

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

2

Q,

or

F=kAv

2

Q.