Bernoulli's equation

[Guest richardcates]

I have been asked to give the formulae and explain using a diagram Bernoulli's equation.

I have been told that the equation is:

 

PT = Pst + Pf + Pv +Ph

 

where

PT = Total pressure

Pst = static pressure

Pf = frictional pressure

Pv =Velocity pressure

Ph = potential pressure

 

I am having trouble as I cannot find this equation in any text.

can someone please help.

[mbeychok]

Richard Cates:

 

A more correct expression of Bernoulli's Theorem is:

 

P1/dg + V1²/2g + Z1 = P2/dg + V2²/2g + Z2 + Hf

 

where:

 

P1 and P2 = the static pressures at points 1 and 2 in the flow direction

d = the fluid density

g = gravitational acceleration

P1/dg and P2/dg = the pressure heads at points 1 and 2

 

V1² and V2² = the fluid velocities at points 1 and 2

V1²/2g and V2²/2g = the velocity heads at points 1 and 2

 

Z1 and Z2 = the elevation heads at points 1 and 2

 

Hf = the frictional head loss between points 1 and 2

 

It is very important to note that:

 

The above expression of Bernoulli's Theorem is only valid when P1 and P2 are in the SI metric pressure units of Newtons per square meter (N/m²) ... such as Pascals (Pa) since 1 Pa = 1 N/m², or such as Bars since 1 Bar = 100,000 N/m².

 

When P1 and P2 are in the USA units of pounds per square foot (psf) then the pressure head terms become P1/d and P2/d. In other words, the gravitational acceleration (g) is not included in the pressure head terms ... however, it remains in the velocity head terms.

 

The reason for the above differences in the pressure head terms between the SI metric expression and the USA expression is that the Newton (N) is a unit of force which includes the gravitational acceleration ... whereas the pounds per square foot (psf) is not a unit of force and does not include the gravitational acceleration.

 

I hope this helps you,

 

Milton Beychok

(Visit me at http://www.air-dispersion.com)

[Kedas]

I just want to add that one of the advantages of writing the formula with heights is that it can easily be represented graphically.

(The total energy is the distance between two parallel lines you draw)

 

it's the same as the more known v²/2 + P/d + gZ = Cte but devided by g

v²/2g + P/dg + Z = H

[fuel pod]

well I dont actually know ur level of understanding....but Mbeychok gave a very complete reply..

If u have to explain the formula using a diagram...u can expalin the flow of an incompressible fluid through an orifice..how the velocity increases and the pressure decreases as the area decreases ..and vice versa....

Also u can explain the height factor by showing flow though water tanks at different heights connected by pipes....

And the friction head depends on he type of material of the pipe or through the material the fluid is flowing...

Important! Bernoulli`s eq is only applicable to incompressible fluids...