# Supersonic Flow in Diverging Nozzle

• NickPorter
Thanks!In summary, at low speeds the velocity of a fluid increases when the area through which it is traveling decreases. This is due to the pressure differential.

#### NickPorter

Clearly, at low speeds the velocity of a fluid increases when the area through which it is traveling decreases. I am curious as to why a fluid traveling faster than the speed of sound increases its velocity when its area is increased. Thank you

Im not 100% sure why, however the reason it works going from big to small is because of the pressure differential. (P1-P2)=(rho/2(V2^2-V1^2)), as you can see the density times velocity needs to equal the pressure difference. so at a higher speed the pressure differential going from small to large may be larger thus needing a larger V2 to keep the ratio equal to the pressure differential. My best guess!

At low speeds the fluid is treated as incompressible, so when the nozzle contracts, the only way for the molecules to get out of the way of one another and conserve mass is by speeding up.

In a compressible flow, that same fluid can change in density, meaning it isn't required to follow the same rules as incompressible flows.

I may be wrong here, as I haven't ever really considered this question aside from what the equations say, but when the area increases, the density decreases and the temperature drops. This is a net loss of energy that is balanced by the resulting increase in kinetic energy.

From my fuzzy recollection of intermediate thermodynamics (and looking it up):

$\frac{dA}{A}=-\frac{dV}{V}(1-M^{2})$

So in the design of a nozzle's cross-sectional area using mass and energy balances, the rate of change in area of the nozzle at any point is related to the area, velocity, change in velocity, and Mach number.

Putting it another way, compressed fluids going through a converging nozzle can only pass through the nozzle at up to Mach 1 (speed of sound in the fluid). This limitation is due to back pressure and "choked flow," meaning the maximum mass flow rate through an orifice is limited to Mach 1 through that orifice. To increase velocity after a throat (minimum area) requires a diverging (supersonic) nozzle which allows the fluid's pressure to drop, reducing back pressure and accelerating the flow. This is of course not taking into account things like normal shockwaves and the like...

http://en.wikipedia.org/wiki/De_laval_nozzle

Not to intrude, but I have a question for Mech. Engineer. How sensative are these to different levels of temperature of the working fluid? In my case, an ICE.

## 1. What is supersonic flow in a diverging nozzle?

Supersonic flow in a diverging nozzle is a type of fluid flow in which the velocity of the fluid exceeds the speed of sound. This occurs when the fluid is compressed and accelerated through a diverging nozzle, resulting in a decrease in pressure and an increase in velocity.

## 2. How does a diverging nozzle achieve supersonic flow?

A diverging nozzle has a gradually increasing cross-sectional area, which allows for the fluid to expand and accelerate as it flows through the nozzle. This expansion causes a decrease in pressure and an increase in velocity, resulting in supersonic flow.

## 3. What are the applications of supersonic flow in diverging nozzles?

Supersonic flow in diverging nozzles is commonly used in aerospace engineering, particularly in the design of jet engines and supersonic aircraft. It is also used in certain industrial processes, such as in supersonic wind tunnels for testing the aerodynamics of objects at high speeds.

## 4. What are the challenges in studying supersonic flow in diverging nozzles?

One of the main challenges in studying supersonic flow in diverging nozzles is the complex nature of the flow. It involves a combination of compressible fluid dynamics, thermodynamics, and heat transfer, making it difficult to accurately model and predict. Additionally, the high velocities and temperatures involved can also pose challenges in terms of experimental measurements and materials used for the nozzle.

## 5. How can the performance of a diverging nozzle be optimized for supersonic flow?

To optimize the performance of a diverging nozzle for supersonic flow, the shape and dimensions of the nozzle must be carefully designed and optimized through computational fluid dynamics simulations and experimental testing. The nozzle should also be made from materials that can withstand high temperatures and pressure differentials, and its internal surface should be designed to minimize friction and shock waves that can affect the flow. Additionally, the inlet conditions, such as the pressure and temperature of the fluid, should be carefully controlled to achieve the desired supersonic flow.