Question

A gardener waters plants by a pipe of diameter 1cm the water comes out at rate of 20cm×cm×cm÷s the reaction force on hand is 0.0051N

Answer 1

Diameter of pipe = 1 cm
Radius will be, r = 0.5 cm = 0.005m
Area of cross-section of the pipe is, A = πr^2
Density of water is, d = 1000 kg/m3
Volume of water coming out per sec is = 20 cm3/s = 2*10^-5 m3/s
Mass of water coming out per sec is,
dm/dt = density × volume/sec
= (1000)(2*10^-5) kg/s =2* 10^-2 kg/s
dm/dt =2*10^-2 kg/s
Now,
Volume/sec = Area × velocity
A = πr2
= 3.14 x (0.000025)
=> 2*10^-5 = (3.14) × (0.000025) × v
=> v = .2548 m/s
Now, force = change in momentum/sec
=> F = d(mv)/dt
=> F = v(dm/dt) [velocity, ‘v’ is constant]
=> F = (.2548)(2*10^-2)
=> F = .005096 N