Fluid Mechanics Velocity at Outlet

[jdawg]

Homework Statement

Water flows through a 1.5 [in] diameter pipe. In a 1.5 [ft] section of the pipe water is injected through the porous walls into the pipe at a velocity of 3 [in/s]. What is the average velocity at the exit if the inlet velocity is 6 [ft/s]?

Homework Equations

The Attempt at a Solution

I used 62.4 lb/ft³ for the density of water.
I calculated the area of the pipe to be A=πR²=0.01227 ft³
m₁=ρAv=(62.4)(0.01227)(6)=4.59 lb/s

A_w=DL=(1.5/12)(1.5)=0.1875 ft^2 I'm not super confident that this area is correct...
m_w=ρA_wv_w=(62.4)(0.1875)(3/12)=2.925 lb/s

Then I used the conservation of mass...
m₁+m_w=m₂
(4.59)+(2.925)=m₂
m₂=7.25 lb/s

Now just plug into formula to get v_out
v_out=(m₂)/(ρA)=(7.52)/(62.4*0.01227)
v_out=9.82 ft/s

Which is wrong... My options are 7 ft/s, 18 ft/s, 28 ft/s, and 150 ft/s.
I'm not sure what I did wrong!

 

[SteamKing]

Homework Statement

Water flows through a 1.5 [in] diameter pipe. In a 1.5 [ft] section of the pipe water is injected through the porous walls into the pipe at a velocity of 3 [in/s]. What is the average velocity at the exit if the inlet velocity is 6 [ft/s]?

Homework Equations

The Attempt at a Solution

I used 62.4 lb/ft³ for the density of water.
I calculated the area of the pipe to be A=πR²=0.01227 ft³
m₁=ρAv=(62.4)(0.01227)(6)=4.59 lb/s

This calculation seems to be OK.

A_w=DL=(1.5/12)(1.5)=0.1875 ft^2 I'm not super confident that this area is correct...
m_w=ρA_wv_w=(62.4)(0.1875)(3/12)=2.925 lb/s

Is the circumference of a circular pipe equal to its diameter? Or is it equal to something else?

 

[jdawg]

Haha I knew that area couldn't be right... I got thrown off because I was given the length of the porous wall. So is that length L just useless information?

 

[SteamKing]

Haha I knew that area couldn't be right... I got thrown off because I was given the length of the porous wall. So is that length L just useless information?

No, it's not the length that's the problem with the calculation.

I mentioned specifically the circumference of the pipe and how you calculated it.

 

[jdawg]

Oops sorry. That makes more sense. Circumference=2πr*h=0.0625ft². Thanks!

 

[SteamKing]

Oops sorry. That makes more sense. Circumference=2πr*h=0.0625ft². Thanks!

What's h supposed to be?

 

[jdawg]

Oops, that's the length L!