4 replies to this topic

[geo123]

A container for water in the form of a wagon is being driven along a frictionless, level track by a jet of water. The jet of water has a horizontal velocity of 30ft s^-1, and the cross-sectional area of the jet is 2 in^2. The jet of water overtakes the wagon, hits the far end of it, and is deflected down into the body of the wagon. No water is spiller; all of it falls down into the wagon. At time zero, the wagon has a velocity of 10ft s^-1, and the mass of the wagon and the water which is in it at that instant is 100lbm. Calculate the time required for the wagon to accelerate from a velocity of 10ft s^-1 to a velocity of 20ft s^-1. Assume that the jet of water follows the wagon and falls into it during all this time. Note that the density of water is 62.4lbm ft^-3.

[geo123]

My working:
The balance at the x-coordinate is
rhoe*v1*A1=rhoe*v2*A2=mass flow rate.
0=-rhoe*v1A1(V-vj)+Fx
F(x)=mdV/dt=rhoe(vj-V)A1vj
d(mV)/dt=rhoe(vj-V)A1vj
Integral of d(mV)=integral of rhoe*(vj-V)A1vjdt
(m0+rhoe(vj-v)at)V(t)=rhoe(vj-V)A1vjt
m0V(t)=(rhoe(vj-V)A1vj-V(t)rhoe(vj-V)t
It leads to a dead end after this as I differentiated V with respect to time.
Then I integrated dV from 10 to 20 and integrated (rhoe(vj-V)A1vj-V(t)rhoe(vj-V))[t]/m0 from 0 to an arbitrary t

Edited by geo123, 07 October 2015 - 10:29 AM.

[Art Montemayor]

Do you expect our Forum members to do your homework assignments for you?

 

If so, what work input have you done on this assignment up to now?  Please show ALL the work you have done in trying to solve this problem.  If you have not done any work on this effort, then you can't be expecting "help".  What you are expecting is someone to do your work for you.

 

Also, please stop posting duplicate threads of the same topic.  I deleted your other duplicate posting.

[geo123]

A1= cross-sectional area of the jet of water.
m0= the initial mass of the moving vehicle with water in it.
V=velocity of the moving vehicle plus water.
vj=velocity of the jet of water.

[geo123]

I didn't consider the momentum at the y-coordinate because the ground is frictionless.