Find Mass Flow Rate: Formula & Explanation from a Rocket

In summary, the conversation is about clarifying the formula for finding the mass flow rate in a rocket, which is \frac{dv}{dt}. The thrust equation is also discussed, which involves the rate of ejected mass flow (q). The variables used in the equations are defined, including v for velocity, M for mass, and q for volumetric flow rate. The link provided offers information on mass flow rates through orifices, as well as the molecular weight of the propellant. The formula for calculating the mass flow rate is also mentioned, which can be either mdot = \frac{A p_t}{\sqrt{T_t}} * \sqrt{\frac{\gamma}{R}} * M (1 + \frac{\gamma
  • #1
.:Endeavour:.
80
1
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 [tex]\frac{dv}{dt}[/tex]. 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:

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

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

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
 
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  • #2
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
 
  • #4
I think this might be another possibility:

[tex]\frac{m_f - m_i}{\Delta t}[/tex]

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.
 
Last edited:
  • #5
yes, this would give you the average mass flow rate. average change of mass (mf-mi) over time (delta t)
 
  • #7
FredGarvin said:
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?
 
  • #8
At is the throat area.
 
  • #9
When you are going to calculate the mass flow rate, which formula do you use? Do you use:

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

or mdot = r*V*A?
 

1. What is the formula for calculating mass flow rate in a rocket?

The formula for calculating mass flow rate in a rocket is: mass flow rate = thrust / exhaust velocity. This formula takes into account the thrust produced by the rocket engine and the speed at which exhaust gases are expelled from the engine.

2. How is mass flow rate related to the overall performance of a rocket?

Mass flow rate is a crucial factor in determining the overall performance of a rocket. A higher mass flow rate means more propellant is being consumed, resulting in a greater thrust and faster acceleration. However, a high mass flow rate also means that the rocket will run out of propellant faster, limiting its flight time and range.

3. Why is it important to accurately calculate mass flow rate in rocket design?

Accurately calculating mass flow rate is essential in rocket design because it allows scientists and engineers to determine the amount of propellant needed for a rocket to reach its desired destination. It also helps in making decisions about the size and type of rocket engine that will be most efficient for a given mission.

4. What factors can affect the mass flow rate in a rocket?

The mass flow rate in a rocket can be affected by several factors, including the design and size of the rocket engine, the type and amount of propellant used, the combustion efficiency of the engine, and the altitude and atmospheric conditions of the flight.

5. Can the mass flow rate in a rocket be increased?

Yes, the mass flow rate in a rocket can be increased by increasing the thrust of the engine or by using a more efficient propellant. However, these changes must be carefully balanced with other factors, such as the weight of the rocket and the cost of the propellant, to ensure optimal performance and efficiency.

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