# Nozzles and Flow Velocity

Hi guys,

I'm no engineer, but I have a question regarding engine thrust and nozzles:

Consider a simple model rocket motor with no nozzle (i.e. just a straight cylindrical pipe with its mass flow coming out the back) that has a mass flow rate of 2kg/s. Since F = v dm/dt we would have dm/dt = 2kg/s and the exhaust velocity would most likely be quite low. Now consider the addition of a convergent-divergent nozzle. My question is this: The effect of the nozzle would be to increase the exhaust velocity, BUT due to the conservation of mass, would the mass flow rate (dm/dt) still be dm/dt = 2kg/s or close to 2kg/s?

SteamKing
Staff Emeritus
Homework Helper
That's why c-d nozzles are useful. In order to maintain the continuity of the mass flow thru the nozzle, the flow must accelerate thru the throat, so Vout > Vin.

enigma
Staff Emeritus
Gold Member
if you have a supersonic nozzle (and I'm assuming you do since there is no other reason to have a divergent portion), then you will choke the flow in the throat. Whether you are close to 2kg/s depends on the design of the rocket, though. It is much more likely that if a straight tube was ejecting 2kg/s, that you will have significantly less mass flow

Wouldn't conservation of mass be broken if the mass flow rate decreases? If the mass flow is decreased with the addition of a nozzle, does that mean that there will be a pressure increase within the motor? I'm guessing that the increase in exhaust velocity more than makes up for the decrease in mass flow.

Gold Member
It depends on your constraints on your question. If the throat area of the nozzle is the same as the cross-section of the hypothetical straight tube, then for a given total temperature and pressure, the mass flow will be the same. Of course with the nozzle, the velocity will be a great deal higher so you'll get more thrust from it.

enigma
Staff Emeritus