ID:-------------Name: --------------
Quiz: Chapter 3
Time: 15 minutes
Course: 58:160, Fall 2012
The exam is closed book and closed notes.
A vane on this moving cart deflects a 10 cm water jet as shown. The initial speed of the water in
the jet is 20 m/s, and the cart moves at a speed of 3 m/s. If the vane splits the jet so that half goes
one way and half the other (cross sections of divided jets are equal and half of initial jet
diameter), what force is exerted on the vane by the jet?    1000 kg/m3 
Solution:
A cart is moving at with steady speed
ID:-------------Name: --------------
Quiz: Chapter 3
Time: 15 minutes
Course: 58:160, Fall 2012
Make the flow steady by referencing all velocities to the moving vane and let the control volume
moves with the vane as shown
We have the relative velocity as 20-3=17 m/s and
v1x  v1
v2 x  v2 cos 45
v2 y  v2 sin 45
v3 y  v3
A1  2 A2  2 A3
Continuity Equation:
v1 A1  v2 A2  v3 A3
v1  2 A2   v2 A2  v3 A2
(2 points)
2v1  v2  v3
Since Q2  Q3 (because half goes one way and half the other) and A2  A3
v1  v2  v3
So we have x and y momentum equations as
x-momentum Equation
Fx  m2v2 x  m1v1
Fx  17 2 cos 45  1000  4   0.12  2  17 2  1000  4   0.12 
(4 points)
 802  2270  1467 N
y-momentum Equation:
Fy  m2v2 y  m3v3 y
Fy  17 1000  sin 45 17  4   0.12  2  17 2  1000  4   0.12  2
 333 N
Total force:
Fwater  1467i+333j N
(4 points)