Pressure Difference: Why Ignored at P1 & P2 in Energy Eqn?

AI Thread Summary
The discussion centers on why the pressure difference at points 1 and 2 is ignored in the energy equation for incompressible fluid flow. It is clarified that pressure and energy are dimensionally different, and the author assumes equal pressure at both points due to their selection being on the surface, where pressure remains constant. The potential energy terms are highlighted as being divided by ρg, leading to the omission of pressure in the calculations. If points were chosen at different heights, the pressures would differ, but the outcome of the equation would remain unchanged. This explanation underscores the assumptions made in applying Bernoulli's equation in this context.
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Homework Statement


why the author ignore the pressure difference at point 1 and point 2 in the energy equation ?pressure at pont 1 must be higher than pressure 2 , right ? as the height of P1 is higher

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foo9008 said:

Homework Statement


why the author ignore the pressure difference at point 1 and point 2 in the energy equation ?pressure at pont 1 must be higher than pressure 2 , right ? as the height of P1 is higher
Pressure and energy are dimensionally different. How would you propose to take pressure into account for an energy equation involving incompressible fluid?
 
haruspex said:
Pressure and energy are dimensionally different. How would you propose to take pressure into account for an energy equation involving incompressible fluid?
sorry , why the author did not take the P/ y into the calculation ? where y = ρg
 
foo9008 said:
sorry , why the author did not take the P/ y into the calculation ? where y = ρg
The 2+ and 1+ are the potential energy terms. It is a bit confusing because the author has divided out ρg everywhere.
 
haruspex said:
The 2+ and 1+ are the potential energy terms. It is a bit confusing because the author has divided out ρg everywhere.
after dividing the ρg why there is no P to be taken into the calculation ? the author assume P1 and P2 as same pressure? why ?
 
foo9008 said:
after dividing the ρg why there is no P to be taken into the calculation ? the author assume P1 and P2 as same pressure? why ?
Bernoulli's equation refers to identified points in the streamline. The author's choice of height values (1, 2) indicates the points being chosen are on the surface, so the pressure is the same. If instead you pick points at the bottom of the stream then the heights are the same and the pressures are different, but the equation turns out the same.
 
haruspex said:
Bernoulli's equation refers to identified points in the streamline. The author's choice of height values (1, 2) indicates the points being chosen are on the surface, so the pressure is the same. If instead you pick points at the bottom of the stream then the heights are the same and the pressures are different, but the equation turns out the same.
so do you mean the author choose point 1 and2 on the surface??
 
foo9008 said:
so do you mean the author choose point 1 and2 on the surface??
It seems that way.
 
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