Effect of Nozzle Design on Mass Flow Rate and Exhaust Velocity

In summary, the addition of a convergent-divergent nozzle to a simple model rocket motor with no nozzle would increase the exhaust velocity, but the mass flow rate (dm/dt) would still be dependent on the design of the rocket and the area ratios of the nozzle. The nozzle must be started before the throat is choked, which requires a higher pressure ratio, but if the areas of the throat and pipe are equal, then equal reservoir conditions will produce the same mass flow rate through the nozzle or the straight pipe. Conservation of mass cannot be broken and the mass flow rate out of the combustion chamber may decrease, but the mass flow through the nozzle will be dependent on various factors.
  • #1
Alexrey
35
0
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?
 
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  • #2
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.
 
  • #3
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
 
  • #4
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.
 
  • #5
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.
 
  • #6
Conservation of mass can't be broken. Your mass flow rate out of the combustion chamber will go down. The mass flow through the nozzle will be dependent on the fuel, operating temperatures and pressures in the combustion chamber, and the area ratios of the nozzle.
 
  • #7
No, the mass flow will not go down in the situation I described. If the nozzle is started, then the throat is choked and it's mass flow is dependent on the total pressure, total temperature and the throat area. Starting a converging-diverging nozzle requires more pressure ratio than choking a straight pipe, so if the pressure ratio is enough to start the nozzle, then the pipe will be choked and it's mass flow equation is identical to the nozzle. In that case, if the areas of the throat and the pipe are equal, then equal reservoir conditions will produce the same mass flow rate through the nozzle or the straight pipe.
 

What is a nozzle and how does it work?

A nozzle is a device that is used to accelerate and direct the flow of a fluid, such as gas or liquid. It typically consists of a converging section, a throat, and a diverging section. When fluid passes through the nozzle, its velocity increases due to the narrowing of the cross-sectional area, causing a decrease in pressure. This increase in velocity and decrease in pressure allows the fluid to be expelled at a high speed, similar to the function of a garden hose nozzle.

What is the relationship between nozzle size and flow velocity?

The size of a nozzle directly affects the flow velocity of a fluid passing through it. A smaller nozzle will result in a higher velocity, as the fluid is forced through a smaller area, while a larger nozzle will result in a lower velocity. This relationship is governed by the continuity equation, which states that the flow rate of a fluid is constant, so as the cross-sectional area decreases, the velocity must increase.

What factors affect the flow velocity of a fluid through a nozzle?

The flow velocity of a fluid through a nozzle is affected by several factors, including the size and shape of the nozzle, the type of fluid, and the pressure and temperature of the fluid. Additionally, the presence of obstructions or irregularities in the nozzle can also affect the flow velocity. Other external factors such as atmospheric pressure and altitude can also impact the velocity of the fluid passing through a nozzle.

What is the ideal flow velocity for a specific application?

The ideal flow velocity for a specific application depends on the purpose of the nozzle. For example, in a rocket engine, a higher flow velocity is desirable to achieve maximum thrust. In a garden hose, a moderate flow velocity is preferred to ensure adequate water pressure without wasting excess water. Ultimately, the ideal flow velocity for a specific application will vary and must be determined based on the desired outcome and the properties of the fluid being used.

What are some common uses for nozzles?

Nozzles have a wide range of applications, including in rocket engines, garden hoses, fire extinguishers, and spray bottles. They are also used in industries such as oil and gas, agriculture, and manufacturing, for tasks such as coating surfaces, cleaning, and cutting materials. Additionally, nozzles are commonly used in everyday household items such as showerheads, faucets, and vacuum cleaners.

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