# Definition of the following Equation?

I have been using the following equation in my assignments to calculate the air flow energy:

(0.5*D*V^2)+P

where:

D= density
V=veolcity
P= Pressure

I understand bernoulis conservation of energy equation is similar to the above however bernoulis equation does not apply to a compresable fluid such as air.

If somebody could explain the proper name of the above equation i would be most gratefull

thanks

tiny-tim
Homework Helper
hi cjh1990! (have a rho: ρ and try using the X2 icon just above the Reply box )
(0.5*D*V^2)+P

that's not an equation (no = symbol) but it looks like part of the standard Bernoulli's equation …

P + 1/2 ρv2

to calculate the air flow energy

Just to reinforce what TinyTim has said.

Not only is your expression not an equation, but it also does not have the dimensions of energy, so if you are trying to use it to calculate energy you will fail.

You are correct in observing that Bernoulli's equation applies to incompressible flow in standard form.
This may be done for air (gas ) flow in certaincircumstances or for short enough periods.
Otherwise you have to take density as a function of time or velocity, not as a constant.

AlephZero
Homework Helper
There are many situations in aerodynamics where it is a reasonable approximation to assume that a gas IS incompressible (though of course real gases are compressible).

As a rule of thumb, it doesn't make much difference for flows with Mach numbers below about 0.2 - unless changes in pressure are an essential part of the way the system is suppposed to operate, like many heat engine cycles for example.

thanks for the reply. Sorry for the poor effort of writing out the equation, im use to writing equations out in microsoft word in the set format. However the equation that tiny tim wrote is what i was trying to get at.

Thanks for all your descriptions that has more than answered my question thanks guys

brewnog
Gold Member
Not sure you understood. Tiny Tim didn't write an equation. An equation has an equals sign in it.

The equation that is required in my assignment to calculate the energy of the internal air flow of a manifold is:

Fluid Energy= P + 1/2 ρv^2

Therfore i understand the bernoulis conservation energy equation, but i canot find a definition/explanation to this equation wich is very similar to bernoulis.

tiny-tim
Homework Helper
hi cjh1990 ! P + 1/2 ρv2 is called the total pressure … it's the sum of the static pressure P and the dynamic pressure 1/2 ρv2

(pleeeease stop calling it an equation … it's an expression, or a formula )

btw, Bernoulli's equation for compressible flow is

P + 1/2 ρv2 + ρgh + ρε = constant along a streamline,

where h is the height, and ε is the internal energy density hi cjh1990! (have a rho: ρ and try using the X2 icon just above the Reply box )

that's not an equation (no = symbol) but it looks like part of the standard Bernoulli's equation …

P + 1/2 ρv2

i also think that is standard Bernoulli's equation....