How to Solve a Fluid Dynamics Problem with Bernoulli’s Equation?

[fysics4fun]

Homework Statement

A very large open water tank has a 50 cm diameter output pipe connected 10 m above the water main which is 6 cm in diameter. If the gauge pressure in the water main reads 9.8 E4 Pa what is the speed at which the water is supplied?
The answer should be 0.5 m/s but I can't see how with Bernoulli's equation. The gauge pressure given is exactly what the pressure change would be (roh g h) when height is the only factor. If the velocity term drops because of no velocity change tho, how can the pipe diameters be different?

Homework Equations

Bernoulli's

The Attempt at a Solution

The gauge pressure given is exactly what the pressure change would be (roh g h) when height is the only factor. If the velocity term drops because of no velocity change tho, how can the pipe diameters be different?

 

[gneill]

Homework Statement

A very large open water tank has a 50 cm diameter output pipe connected 10 m above the water main which is 6 cm in diameter. If the gauge pressure in the water main reads 9.8 E4 Pa what is the speed at which the water is supplied?
The answer should be 0.5 m/s but I can't see how with Bernoulli's equation. The gauge pressure given is exactly what the pressure change would be (roh g h) when height is the only factor. If the velocity term drops because of no velocity change tho, how can the pipe diameters be different?

Homework Equations

Bernoulli's

The Attempt at a Solution

The gauge pressure given is exactly what the pressure change would be (roh g h) when height is the only factor. If the velocity term drops because of no velocity change tho, how can the pipe diameters be different?

Hmm. As you say, the pressure in the inlet pipe corresponds to a head of water that is the same as the supposed elevation of the outlet pipe above it. Perhaps the precise geometry becomes significant. Is the 10m pipe separation center to center? Top of one to the bottom of the other? Is the outlet pipe actually full? Does it empty into free air, or an open pond at the same level? Is the pressure change with depth across the face of the outlet pipe significant (different flow rates across its cross-section)?

 

[fysics4fun]

We are not provided any details other than the problem stated just as it is. I am a teacher, and I put this question on Friday's exam (as extra credit) without looking at it very closely, unfortunately (it looks easy at first glance!) Now I have to explain it tomorrow and I don't know how :P
I'm starting to think it's just a badly written problem, but I'd like a few more responses to give me confidence that I'm not missing something.

I REALLY appreciate your input- I've been dying waiting to hear from people...