Water pressure in tank with open pipe

[JaySR]

We are trying to pressurise a tank of water to simulate (in a lab) pressure at approx. 5m deep in a river. If the tank is full of water and closed, apart from an open topped pipe that extends 5m vertically from the top of the tank, would the pressure 0.1 m down into the tank be: density of water x gravity(9.81) x 5.1m (assuming the pipe was full of water)? Does the diameter of the pipe above the tank have any effect on the water pressure in the tank?

The cross-sectional area of the tube is small in comparison to the tank. My understanding is that the pressure in the tank would be the same regardless of the diameter of pipe used. However, it doesn't seem right that, for example, a 20mm diameter pipe full of water and extending 5m above a 10m^3 tank would pressurise the tank to the same extent as pipe 2m in diameter filled (with a far greater weight of water) to the same height?

 

[GeoPaveTraffic]

As long as the pipe is large enough so that surface tension does not change the pressure, then the diameter has no effect on the pressure.

Mike Lambert

 

[bimr]

No, the pressure is not affected by the diameter of the pipe.

Fundamentals of Hydraulics: Pressure


For a given depth, pressure is independent of the shape and size of the container (see below). This concept was first recognized by French scientist Blaise Pascal (1623– 1662).

 

[LittleInch]

You're confusing pressure (force per unit area) with weight or total force. Yes your 2m diam pipe will exert a lot more total force or weight, but this is spread over a much larger area. An elephant weighs 30 to 40 times a human, but does it sink into the ground - no because it's total foot area is approx. 30 times a human foot (it has more feet as well) so it's ground pressure is similar ( and much less than a stiletto heel....)

One thing you will need to be careful of is that with a small tube and large tank, the level of the water could change a lot based on only a small change of temperature. Hence a small increase in temperature could result in a higher level if the pipe is actually taller than 5m or less pressure if the water cools and the level in the pipe reduces.

You might be better off with a small header tank fitted with a ball valve and an overflow to maintain a constant level - think of a gravity fed central heating system.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[bimr]

Pressure is independent of the shape and size of the container and is dependent solely on the height of the container. The example of the elephant seems to be inappropriate.

 

[LittleInch]

I agree with the diagram as this is basic physics. The man elephant thing is just a way to demonstrate the bigger total weight versus bigger square area thing results in the same pressure, which is what is confusing the OP.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[JaySR]

Thanks for the replies everyone. The purpose of the set-up is to acclimatise fish to a certain pressure. For argument's sake, imagine this scenario: A 1m^3 cube tank with a straw extending up by 5m full of water. Ignoring the effects of surface tension, will a fish in the middle of the 1m^3 tank experience pressures of 1000kg/m^3 x 9.81N/kg x 5.5m? Even though the cross-sectional area of the water column in the straw, creating the pressure, is much smaller than cross-sectional area of the fish? Should the cross-sectional are of the pipe/tube used to create the pressure in the tank be at least equal to the area of the fish or does it not matter? I understand that pressure is independent of the shape of the container as in the diagram above, but in terms of the corresponding forces on the fish, instinctively it seems like the cross section of the water column in the pipe should be at least equal to the the area of the fish.

What's throwing me off is that in usual problems, an object subjected to some water pressure is normally smaller in area than the cross-sectional area of the water above it (a diver in the sea, a submerged penstock in a river etc.

Thanks in advance.

 

[LittleInch]

I would use something a bit bigger than a "straw", but otherwise pressure is pressure, it applies equally in all directions from a single point and it doesn't vary by area in the way you're talking about.

So in answer to your questions,
Will a fish experience a pressure equivalent to 5.5m of water head - Yes
Even though the X sectional area is different - Doesn't make any difference
Should the area be the same - No doesn't make any difference

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[BUGGAR]

What keeps the fish from swimming up the straw if the pressure gets too much for him. I wish we had an office like that.

 

[JaySR]

Ok thanks LittleInch. We definitely won't be using a straw, that was just to emphasise the difference in size between the tank and the pipe.

The straw (pipe) will be too small for the fish to swim up, they will be introduced into the tank through sealed door.

 

[77JQX]

Note that it doesn't even need to be a straight pipe. You can use a hose to go out the door, up the stairs, and over and around any obstacles you need to get your 5m height. As long as the hose (or pipe) doesn't have any air in it, and the water surface in the hose is 5m above the tank, then you get the 5m pressure you desire.

 

[Compositepro]

This thread covers some very basic, but important, engineering principles. One thing that I have observed over time is that many engineers do not clearly understand the difference between stress and pressure, both of which have units of force per unit area, but do not mean the same thing. Stress is the term that should be used for solid materials. In solids the stresses at any point can be different in various directions. What makes a fluid a fluid is that the pressure at any point is the same in all directions (because shear strength is zero). In the real world there are many semisolid materials which may act as solids or as fluids depending on time scale and temperature. Generally, using the term pressure implies that you are dealing with a fluid, but there are plenty of exceptions this, leading to some confusion.

 

[BigInch]

Pressure has nothing inherently to do with a fluid. Pressure is force per unit area, whether that force is applied by weight of atmosphere above, or an elephant.

Stress is developed by resistance to deformation. Fluids exhibit shear strength when subject to deformation, so it is not always zero, as when the fluid is moving. Movement of fluids and semi-solids is resisted by its shear strength which of couse is described by viscosity. Semi-solids have a relatively high viscosity and can require signnificant force being applied to deform them, wile on the other hand the viscosities of air and water are relatively low and deform readily at low shear stresses.

 

[BUGGAR]

Fluids are solids with zero shear strength.

 

[bimr]

In physics, a fluid is a substance that continually flows under an applied shear stress. Fluids are a subset of the phases of matter and include liquids, gases, plasmas and, to some extent, plastic solids. Fluids can be defined as substances that have zero shear modulus or in simpler terms a fluid is a substance which cannot resist any shear force applied to it.

Pressure is defined as force per unit area. It is usually more convenient to use pressure rather than force to describe the influences upon fluid behavior.

 

[itdepends]

A query for JaySR- how long are the fish going to be in the 1m3 container and how are you going to measure/control the dissolved oxygen/other dissolved gases content?

It's not just the fish that will need to "acclimatise" I would assume that the dissolved gases content of the water increases as you increase the pressure (a quick Google search confirms this). Unlike in nature where the fish would be moving from lower pressure environment to a high pressure environment- here (I assume) you are changing the pressure of the environment.

By the way- 5m down isn't very far from the perspective of a fish.

As a chem eng/metallurgist the first part of any answer I give starts with "It Depends"

 

[JaySR]

I'm not sure how long the fish will be acclimatised for, the biologist is sorting that one out. The fish will be kept in holding tanks, they will then be introduced into the smaller tank and filled with the same water so the tank and 5m high pipe are full. The time taken to fill the pipe will be long enough so the fish is not subjected to a 'pressure shock'. The dissolved oxygen concentration will be measured using a probe in the holding tanks. An aerator might be used in the acclimatising tank a well if necessary.

The fish are being passed through a 'fish friendly' turbine which operates at a maximum of 5m of water head, this is why we are acclimatising the fish to 5m in the lab set-up.