Question

A projectile-like object with maximum diameter of 20 cm is placed at the exit of a 25-cm-diameter pipe. Water flows through the pipe. At the upstream location 1, the velocity is uniform and equal to 2 m/s. The water exits to the atmosphere where the pressure is 100 kPa. Find the force required to hold the object in place. Be sure to state your assumptions. Be explicit in defining your control volume - remember that the CV must be defined so that an external force can be defined. (See additional documentation regarding the choice of a control volume. For extra credit, show that the analyses from the two CV's are consistent with each other; i.e., show that the force on the projectile is the integrated pressure over its surface, as would be expected.)

Answer 1

349.07 N

Step-by-step explanation:

Inlet area,
`A_i=\frac {\pi (d_i)^(2)}{4}=\frac {\pi * 0.25^(2)}{4}= 0.049087 m^(2)`

Outlet area,
`A_o=\frac {\pi (d_o)^(2)-(d_i)^(2)}{4}=\frac {\pi * 0.25^(2)-0.2^(2)}{4}= 0.017671 m^(2)`

`A_iV_i=A_oV_o`

0.049087*2=0.017671v_o[/tex]

`v_o=\frac {0.049087*2}{0.017671}=5.555556 m/s`

Mass flow rate=
`\rhoA_iV_i=1000*0.049087*2=98.17477 Kg/s`

`F_x=98.17477(v_o-v_i)= 98.17477(5.555556-2)= 349.0659 N\approx 349.07 N`