Please help with Physics?

Question

If a pipeline has an entrance of 2’ and exit of 1', water flows into the entrance at 100ft/sec. The pressure at the entrance is 200lbs/ft2 what is the velocity and pressure at exit? (Density of water is 62 lb/ft3). I know I need to use Bernoulli's Principle but I do just not understand how to plug in the numbers

Answer 1

This looks like a nonsensical made up question. However, ignoring the numbers, just set it up like this:

Exit velocit is obviously 4x the inlet velocity. So,

v1^2 / 2g + p1 / rho = v2^2 /2g + p2 /rho

(100)^2 / (2*32.2) + 200 / 62 = (400)^2 / (2*32.2) + p2/62

solve for p2 (don't bother, its nonsense)

Answer 2

In this instance as stated you do not need Bernoulli; continuity and plane geometry will do just fine. IF this water is flowing in the same volume is also flowing out. IF it is flowing in at 100 fps, thru a 2'dia. entrance it will be flowing out at 400 fps as it enters the 1'dia exit. The two areas are proportional to the squares of the diameters. The velocities as given are unrealistically high. Even practical pipeline flows of 20 fps are extreme.
You cannot calculate the flowing pressure near the exit because the pressure loss within the pipe cannot be calculated without knowing the length. However at the velocities shown the unit pressure loss would be immense.
Looking further at just the only pressure given , the one at the inlet and the two diameters we will try again. Only about half of the absolute pressure can be converted to velocity due to the critical flow restriction. So about half of 215 psia would be around 107 psia or 247 ft of water equivalent. The sharp edge orifice Velocity would be 0.6 XSq rt of (2X32 X247) or no more than about 125 fps.
The critical velocity for water flowing thur a nozzle is therefore much less than the 400 fps as above. So the actual entering velocity can be no more than 125/4 or 31 fps, not 100fps

Answer 3

You don't need Bernoulli's Principle. Whatever goes in in a given time must come out in that same time. That's all you need to know.

Answer 4

of the exit is half the entrance...what do you think?