A horizontal water jet of constant diameter 0.1m with speed 10 m/s enters a cont

Question

A horizontal water jet of constant diameter 0.1m with speed 10 m/s enters a container which is moving toward the stationary nozzle at a speed of 2m/s. At t = 0 the container is 2m from the nozzle exit. Taking the container as a control volume with one inlet, at t = 0.2 sec find: (a) the amount of water (kg) which has entered the container; (b) the amount of x momentum into the container which has gone into the container. (c) the distance of the container from the nozzle at t = 0.2 sec. Approx. Ans.: (a) total mass 24 kg; (b) total x mom: 200 kg m/s; (c) apart at t = 0.2sec: x 1.4 m

Explanation / Answer

part a:

relative speed of container w.r.t. nozzle=10+2=12 m/s

then water that has entered the container

=area of the outlet*relative speed*time

=pi*(0.1/2)^2*12*0.2=0.018849 m^3

then mass=volume*density=0.018849*1000=18.849 kg

part b:

total momentum=mass entered*speed

=18.849*12=226.194 kg.m/s

part c:

distance of container from the nozzle at t=0.2 seconds

=2-2*0.2=1.6 m

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