Impact of a jet onto vanes
The liquid comes out in the form
of a jet from the outlet of a nozzle, which is fitted to a pipe through which
the liquid is flowing under pressure. If some plate, fixed or moving, is placed
in the path of the jet, a force is exerted by the jet on the plate. This force
is called impact of jet, and is obtained from Newton’s second law of motion or from
impulse-momentum equation.
Force exerted on the inclined
plate, moving with a uniform velocity in the direction of a the jet
V = absolute velocity of jet of water
u = velocity of the plate in the direction of jet
a = cross-sectional area of jet
θ = angle between the jet and the plate
Relative velocity of the jet = V-u
Mass of water striking per second
= ρa(V-u)
If the plate is smooth and loss
of energy due to impact of the jet is assumed to be zero, the jet of water will
leave the inclined vane with a velocity equal to (V-u).
Force exerted by the jet in the
direction normal to the plate is given as Fn
= Mass striking pr second × (initial velocity in the normal direction with
which jet strikes – final velocity)
= ρa(V-u)[ (V-u)sin θ – 0)] = ρa(V-u)2sin θ
This normal force can be divided
into two components namely Fx and
Fy in the direction of jet
and in a direction perpendicular to the jet respectively.
Fx = Fn sin θ = ρa(V-u)2sin2
θ
Fy = Fn cos θ = ρa(V-u)2sin θ cos θ
Work done per
second by the jet on the plate = Fx
× (Distance per second in x-direction)
= Fx × u = ρa(V-u)2sin2
θ × u = ρa(V-u)2.u.sin2 θ kgf-m/sec or N m/s.