Why is pressure difference ignored at points 1 and 2 in the energy equation?

[foo9008]

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

Homework Equations

The Attempt at a Solution

 

[foo9008]

notes attached here

 

[haruspex]

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?

 

[foo9008]

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

 

[haruspex]

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.

 

[foo9008]

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 ?

 

[haruspex]

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.

 

[foo9008]

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??

 

[haruspex]

so do you mean the author choose point 1 and2 on the surface??

It seems that way.