Flow From a Tank through a Pipe

[kicks66]

Im looking to create a program which models a tabletop water tunnel. One part of the system involves flow out of a tank through a pipe. So far I have used the assumption that the pressure in the pipe is the same as atmospheric but I feel this is wrong, and therefore my use of SQRT(2*g*height difference) is incorrect to calculate the velocity out of the pipe. How would I go about finding the pressure in the pipe? And how would I take into account surface roughness effects along the length of pipe?

 

[anorlunda]

The pressure varies through the pipe. In fact, the pressure gradient is what makes the water flow.

At the tank end, yes the pressure is dependent on "head" meaning the pressure dependent on height of the tank.

At the far end, yes pressure is pretty close to atmospheric.

Yes roughness matters, but in proportion to flow. The rougher the surface the more resistance to flow. If your tank has fixed height, the the resistance of the pipe determines how fast the water flows out.