- #1
Sir James
- 7
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I’m confused as to how energy per unit weight can be quantified as a head of fluid. I have tried to understand this from a couple of angles but am getting confused. I’ll go through my methodology to see where you can spot the cracks.
If energy = work done = (force * length over which it acts) then pressure energy of a fluid is Pressure*Area*Length
A column of water exerts a downward force, being its weight, and so the pressure required to support a column of water is equal to the weight of the column divided by the base area of the column. So, if the pressure exerted by the column of water is equal to
mass density*gravity*height
then the pressure at the bottom is equal to
mass density*gravity*height
but acts vertically upward. The energy of the fluid supporting this head would then be
pressure*area*length = mass density*gravity*height*area*length
However, what is confusing me is what the final term length is. From my reading it seems to suggest that the column of water is the governing factor, in which case the length would be the height of the column so the pressure energy would be:
mass density*gravity *area* height^2
However, on looking at a column of water I just can’t see how this is correct. If the column was split into incremental parts then surely the pressure which acted upward would only move 1 increment by a distance of the height (to the top) whereas another increment would only be moved halfway up the column? Does this not mean that the pressure energy at the base of the column would be more like force*average distance over which it acts, i.e. height/2?
Cheers for the help
If energy = work done = (force * length over which it acts) then pressure energy of a fluid is Pressure*Area*Length
A column of water exerts a downward force, being its weight, and so the pressure required to support a column of water is equal to the weight of the column divided by the base area of the column. So, if the pressure exerted by the column of water is equal to
mass density*gravity*height
then the pressure at the bottom is equal to
mass density*gravity*height
but acts vertically upward. The energy of the fluid supporting this head would then be
pressure*area*length = mass density*gravity*height*area*length
However, what is confusing me is what the final term length is. From my reading it seems to suggest that the column of water is the governing factor, in which case the length would be the height of the column so the pressure energy would be:
mass density*gravity *area* height^2
However, on looking at a column of water I just can’t see how this is correct. If the column was split into incremental parts then surely the pressure which acted upward would only move 1 increment by a distance of the height (to the top) whereas another increment would only be moved halfway up the column? Does this not mean that the pressure energy at the base of the column would be more like force*average distance over which it acts, i.e. height/2?
Cheers for the help