Is head from a larger reservoir greater or the same?
Calling all crazy engineers. Here is the situation. My brother (John) and I had a debate (OK, an argument) about whether a pipe from a dam on the hill would deliver water at the same velocity as from a virtual tank (e.g. a 30,000 litre water tank) beside it, assuming the same depth and elevation.
The purpose of the debate was to establish whether a smaller guage, and therefore, cheaper, pipe might be able to be used to deliver water to the micro-hydro electricity generator that he wants to power his eco-friendly home with.
John argued that, assuming that the depth and elevation of the two bodies of water are the same (and all other factors being equal, except the volume of water in the dam), the velocity of the water at the micro-hydro would be the same in both instances on the understanding the water velocity is the product of hydraulic head which is the weight of a column of water directly above the outlet plus any pressure due to gravity.
However, I argued that, because liquids exert pressure equally in all directions, the weight of the water in the (much larger) dam - let’s say, 3 million litres - that is above the exit point (anywhere in the dam) will add to the velocity of the water at the micro hydro. This, I reasoned, would allow him to use a smaller, cheaper, pipe because he could use a smaller amount of water, at a higher velocity, to generate his power.
To test my hypothesis, I performed a simple test in my laundry with two plastic containers representing the tank and the dam. Container A. (the tank) has a volume of 2.5 litres and container B. (the dam) is the same height but is broader and has a volume of 8 litres. Both containers are 31.75 cms tall. I simply drilled an 8mm hole in each container 1 cm from the bottom for the outlet (without a tap or other mechanism to direct the flow of the water).
On releasing the stoppers I found that the stream from Container B. travelled approximately 2-3 cms further than the stream from Container A. but, given the much larger volume of water in Container B. I expected the difference to be greater so I consider the test to be inconclusive.
I have tried to nut this out with reference to several authoritative web sites but it is breaking my non-engineer brain so I would be grateful for your collective assistance.
Who is correct? John or me?
The purpose of the debate was to establish whether a smaller guage, and therefore, cheaper, pipe might be able to be used to deliver water to the micro-hydro electricity generator that he wants to power his eco-friendly home with.
John argued that, assuming that the depth and elevation of the two bodies of water are the same (and all other factors being equal, except the volume of water in the dam), the velocity of the water at the micro-hydro would be the same in both instances on the understanding the water velocity is the product of hydraulic head which is the weight of a column of water directly above the outlet plus any pressure due to gravity.
However, I argued that, because liquids exert pressure equally in all directions, the weight of the water in the (much larger) dam - let’s say, 3 million litres - that is above the exit point (anywhere in the dam) will add to the velocity of the water at the micro hydro. This, I reasoned, would allow him to use a smaller, cheaper, pipe because he could use a smaller amount of water, at a higher velocity, to generate his power.
To test my hypothesis, I performed a simple test in my laundry with two plastic containers representing the tank and the dam. Container A. (the tank) has a volume of 2.5 litres and container B. (the dam) is the same height but is broader and has a volume of 8 litres. Both containers are 31.75 cms tall. I simply drilled an 8mm hole in each container 1 cm from the bottom for the outlet (without a tap or other mechanism to direct the flow of the water).
On releasing the stoppers I found that the stream from Container B. travelled approximately 2-3 cms further than the stream from Container A. but, given the much larger volume of water in Container B. I expected the difference to be greater so I consider the test to be inconclusive.
I have tried to nut this out with reference to several authoritative web sites but it is breaking my non-engineer brain so I would be grateful for your collective assistance.
Who is correct? John or me?
Replies
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2010mayanThe Storage Volume of the reservoir has got nothing to do with the Velocity or pressure at the discharge end of the penstock pipe.
The difference in height between inlet and outlet , ' HEAD ' influences the velocity at the discharge end.
Smaller the tube more the friction loss in HEAD.
Hence with smaller tube the velocity and discharge will be dispropotionately less.
Mayan -
CloudMistOK, thanks Mayan.
Looks like I will have to eat humble pie.
Cheers. -
raj87verma88Like Mayan said, 'Head' is the height of the water coloumn.
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CloudMistThanks for that. I had already understood that principle but was lead to believe that the weight of the remaining water in the dam, applying equally in all directions, would also add force to the water exiting through the outlet pipe. See these links:
Relationship of Force Pressure and head
Hydraulic Head
Rgds. -
AshNZTo think about his mathematically, look at the bernoulli's equation. Bernoulli's equation does not take storage volume into account when calculating velocity.
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