Water Pressure in Conical Tank Question

[Another God]

I was wondering if anyon could help me out.

You have a conical tank with a top diameter of 1m, going down to an outlet of 150mm diameter, height of the tank = 3m, and it's full of water. Assuming an air pressure of 15psi, what is the pressure at the 150mm opening? (the bottom)?

Does the air pressure make a difference due to the nozzle shape of the tank?

Thanks

 

[sridhar_n]

...

Are you trying to say something about a pipeline with a wider beginning and a narow end. The water is flowing from the wider end to the narrower end.

If this is the problem, then u can use bernoulli's theorem,
The total energies at both the ends are the same.

i.e the sum of pressure energy, kinetic energy and potential energy is constant throughout the flow.

in other words:

(p^2)/w + gh + (v^2)/2g is always a constant. Assuming that flow is downwards in the problem, the height of the 1m openong is 3 m and that of the 150mm end is 0. So using this find the total energy on each side and equate them. Since the same fluid is flowing w-the sp.density is the same. p is the pressure. At the opening the pressure = air pressure.
v is the velocity. To find the value of v at both the ends (or atleast cancel out the v term in the equation) u need to use the continuity equation A1*v1 = A2*v2. Using this find, v1/v2, substitute the other values and then find the value of the pressure at the other end.

Got it?

Sridhar

 

[Another God]

Yep, that exactly what we meant.

Thanks for the reply, we'll run some numbers, and get back to you with what conclusions we reach.

Thanks again.

 

[russ_watters]

Originally posted by Another God
Does the air pressure make a difference due to the nozzle shape of the tank?

Nope. Thats one of the trick questions in fluids. Remember - pressure is pressure. The pressure (static and velocity are the same for the various cases you could do here, conveniently) at the bottom is simply the weight density of water times the height. Technically, that's the static pressure, but if the water is flowing, the static pressure at the bottom of the tank is equal to the velocity pressure. So from that you can caluclate the velocity of the water and the flowrate.