Answer:
The resultant force is 2620.05 lbf acting to the right.
Explanation:
The area for inlet section is:
The area for oulet section is:
The volumetric flow rate is:
Q=V1A1=15*0.79=11.85 ft^3/s
The velocities and areas at the exit is the same:
Q=V2A2+V3A3=2V2A2
Clearing V2:
V2=V3=Q/(2*A2)=11.85/(2*0.196)=30 ft/s
The mass flow rate through inlet is:
m1=ρA1V1=1.94*15*0.79=22.99 lbf*s/ft
The mass flow rate through outlet is:
m2=m3=m1/2=22.99/2=11.49 lbf*s/ft
The x-component of force is:
Rx+p1A1=-V1m1
Where p1 is the pressure at inlet
Rx=-(15*22.99)-(2880*0.79)=-2620.05 lbf
Fx=-Rx=2620.05 lbf
The y-component of force is:
Ry+p2A2-p3A3=V2m2-V3m3
Ry+0-0=(30*11.49)-(30*11.49)
Ry=0
Fy=Ry=0
The resultant force is:
This force is acting to the right.