# Mass flow rate formula

#### .: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:

$$0 = \frac{[(M - \Delta M)(v - \Delta v) + \Delta Mu] - Mv}{\Delta t}$$

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

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

#### .: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.

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#### redargon

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

#### .: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?

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