Find Mass Flow Rate: Formula & Explanation from a Rocket

[.:Endeavour:.]

I want to clarify this because I'm still not sure how to find the mass flow rate, for instance from a rocket. I still puzzled from the formula that describes the mass flow rate which is \frac{dv}{dt}. This the formula that I'm currently looking over but I'm not sure if its this formula to find the mass flow rate which is:

<br /> 0 = \frac{[(M - \Delta M)(v - \Delta v) + \Delta Mu] - Mv}{\Delta t}<br />

Then to find the thrust you use this equation:
F_thrust = qV_e + (P_e - P_a)A_e

Where q is the rate of the ejected mass flow which I want to find out.

This is where I got the information: http://www.braeunig.us/space/propuls.htm

 

[redargon]

is there a little more definition of the variables used?

is v the final velocity and u the initial velocity? is M = mass? seems strange.

mass flowrate is mdot or dm/dt (ie. change in mass over change in time)
volumetric flowrate is dV/dt (ie. change in volume over change in time)

if v is velosity, then dv/dt is acceleration, so this is why I'm asking for your variable definitions.

obviously volumetric flowrate is density dependant and mass flowrate is not.

V=m/rho where rho is density.

The thrust equation is related to areas and pressures.
My guess would be:
Pe is pressure at nozzle exit
Pa is Pressure of atmosphere
Ae is cross-sectional area of rocket nozzle

F=PA in simple terms, so that half of the equation is right, but then for the firts term to hold, q would have to be mass flow rate. Usually q is volumetric flowrate, but fine.

Maybe a look at mass flow rates through orifices will help you understand it a bit better. Rocket nozzles are generally orifices with well designed entrances and exits. try: http://en.wikipedia.org/wiki/Orifice_plate

 

[redargon]

check out: http://en.wikipedia.org/wiki/Rocket_engine_nozzle too

 

[.:Endeavour:.]

I think this might be another possibility:

\frac{m_f - m_i}{\Delta t}

Ok, I read over the link that you send me and I found out that mass flow rate units are kg/s. So I think the you subtract mass final from mass initial and divided over the period of time. I'm not sure yet, but this is my assumption.

 

[redargon]

yes, this would give you the average mass flow rate. average change of mass (mf-mi) over time (delta t)

 

[FredGarvin]

Like was already mentioned, you still need to know something about the make up of the propellant, i.e. molecular weight.

Here's what you need:
http://www.grc.nasa.gov/WWW/K-12/airplane/mflchk.html

 

[.:Endeavour:.]

Like was already mentioned, you still need to know something about the make up of the propellant, i.e. molecular weight.

Here's what you need:
http://www.grc.nasa.gov/WWW/K-12/airplane/mflchk.html

Yeah, that's the mass flow rate formula to find the flow rate. Yeah, this are the graphs that I'm looking at for the propellants that each have a unique Optimum Mixture Ratio, Adiabatic Flame Temperature, Gas Molecular Weight, and Gas Molecular Weight. I'm just looking over the Adiabatic Flame Temperature for Kerosene LO₂, LH₂ and LO₂, and also Dinitrogen Tetroxide & Aerozine 50. The area that the formula gives, is it for neck of the engine?

 

[FredGarvin]

At is the throat area.

 

[.:Endeavour:.]

When you are going to calculate the mass flow rate, which formula do you use? Do you use:

mdot = \frac{A p_t}{\sqrt{T_t}} * \sqrt{\frac{\gamma}{R}} * M (1 + \frac{\gamma - 1}{2} M^2)^-^\frac{\gamma + 1}{2(\gamma - 1)}

or mdot = r*V*A?