Forces exerted by a jet on numerical
The forces exerted by a jet on a flat plate numerical
Q.1) Determine the forces exerted with a jet of water of diameter 75 mm at a stationary flat plate, if the jet strikes the plate commonly with a velocity of 20 m/s.
Given
- Diameter of nozzle, d = 75 mm = 0.075 m,
- The velocity of the jet, V =20 m/s
Solution
- Area,
A = (π/4) d^2
A = (π/4) x (0.075)^2
A = 0.004417 m^2
- The force exerted by the jet of water on a stationary vertical plate is given as
F = ρAV^2
- where, ρ = 1000 kg/m3
F = 1000 x 0.004417 x 202 N
= 1766.8 N
=1.7668 kN
- The forces exerted by a jet is 1.7668 kN
Q.2) Water is flowing through a pipe at the end of which a nozzle is fitted. The diameter of the nozzle is 100 mm and the head of water at the centre nozzle is 100 m. Determine the force exerted by the jet of water on a rigged vertical plate. All coefficient of velocity is given as 0.95.
Given
- Diameter of nozzle, d = 100 mm = 0.1 m,
- Head of water, H = 100 m,
- Co-efficient of velocity, Cv = 0.95
Solution
- Area of the nozzle,
a = (π/4)d^2
= (π/4) (0.1)^2
= 0.007854 m^2
- The theoretical velocity of a jet of water is given as
Vth = 44.294 m/s
- The actual velocity of a jet of water,
V = Cv x Vth
V= 0.95 x 44.294
V= 42.08 m/s.
- Force on a fixed vertical plate is given as
F = ρav2
= 1000 x 0.007854 x 42.082
= 13907.2 N
= 13.9 kN
- The force exerted by the jet of water on a fixed vertical plate is 13.9kN
