Water Pressure in Conical Tank Question

In summary, the conversation discusses a problem with a conical tank full of water and an outlet of 150mm diameter. The question is what is the pressure at the bottom of the tank, given an air pressure of 15psi. The solution involves using Bernoulli's theorem and the continuity equation to find the velocity of the water and calculate the pressure at the bottom. It is also mentioned that nozzle shape does not affect the pressure in this scenario.
  • #1
Another God
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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
 
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  • #2
...

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:

[tex](p^2)/w + gh + (v^2)/2g [/tex] 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
 
  • #3
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.
 
  • #4
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.
 

1. What is water pressure in a conical tank?

The water pressure in a conical tank is the force exerted by the weight of the water on the bottom of the tank. It is measured in units of force per unit area, such as pounds per square inch (psi) or Newtons per square meter (N/m²).

2. How is water pressure calculated in a conical tank?

The water pressure in a conical tank can be calculated using the formula P = ρgh, where P is the pressure, ρ is the density of water, g is the acceleration due to gravity, and h is the height of the water column in the tank.

3. What factors affect water pressure in a conical tank?

The water pressure in a conical tank is affected by the height of the water column, the density of the water, and the gravitational acceleration. The shape and size of the tank may also play a role in the distribution of pressure.

4. How does water pressure change in a conical tank?

In a conical tank, the water pressure increases as the height of the water column increases. This is because the weight of the water is concentrated at the bottom of the tank, creating a greater force per unit area compared to a tank with a smaller height.

5. Can water pressure in a conical tank be controlled?

Yes, water pressure in a conical tank can be controlled by adjusting the height of the water column or by changing the density of the water. It can also be controlled by altering the shape or size of the tank to evenly distribute the pressure. Additionally, external factors such as atmospheric pressure and temperature may also affect the water pressure in a conical tank.

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