Choking in a Circular Orifice Plate in a pipe

[boka33]

The equation I have for velocity through a circular orifice plater is as follows:

$$Ud = \frac{Yi\timesC}{\sqrt{(1-(d/D)^4)}}\sqrt{\frac{(2\times(P_{2}-P_{1})}{\rho}}$$

To my understanding, flow becomes choked when this velocity exceeds a Mach number of 1, and is no longer sub-sonic.

Intuitively, decreasing orifice diamter would increase the likelyhood of choke (at least in my mind), but this does not seem to be the case.

If d/D is decreased, the denominator becomes larger, and the velocity becomes smaller, in turn yielding a smaller mach number.

Can anyone explain this so that it make more intuitive sense to me, or tell me if my thouhgt process is off.

Thanks alot

 

[AndyW]

Your equation for velocity through a circular orifice plate is correct and is commonly used in fluid mechanics calculations. The Mach number, which is the ratio of the flow velocity to the speed of sound, is indeed an important factor in determining the flow behavior through an orifice.

As you have correctly pointed out, when the velocity through the orifice exceeds the speed of sound, the flow becomes choked and can no longer be considered subsonic. This is because at this point, the flow velocity is equal to the speed of sound and any further increase in velocity would result in a supersonic flow, which behaves very differently from a subsonic flow.

Now, to address your question about the effect of decreasing the orifice diameter on the likelihood of choke, let's take a closer look at your equation. The term (d/D)^4 in the denominator represents the ratio of the orifice diameter to the pipe diameter. As this ratio decreases, the denominator becomes larger, which in turn decreases the overall velocity through the orifice. However, this also means that the Mach number decreases, making it less likely for the flow to become choked.

In other words, decreasing the orifice diameter decreases the velocity, but it also decreases the likelihood of choke. This is because the denominator in your equation is not the only factor that affects the flow behavior. The term (P2-P1)/ρ represents the pressure difference between the two sides of the orifice, and as this pressure difference increases, the velocity also increases, making it more likely for the flow to become choked. So, while decreasing the orifice diameter may decrease the velocity, it may also decrease the pressure difference, resulting in a lower Mach number and a lower likelihood of choke.

I hope this explanation helps clarify your understanding. Keep in mind that there are other factors that can also affect the flow behavior through an orifice, such as the properties of the fluid and the geometry of the orifice. It is important to carefully consider all these factors when analyzing fluid flow through an orifice.

 

[sir-pinski]

Your equation for velocity through a circular orifice plate is correct. However, the concept of choking in fluid flow is a bit more complex than just the velocity exceeding a Mach number of 1. Choking occurs when the flow reaches its maximum possible velocity, which is also known as the critical velocity. This critical velocity is dependent on the density and pressure of the fluid, as well as the geometry of the orifice.

In your equation, the term (1-(d/D)^4) in the denominator is known as the contraction coefficient, which takes into account the geometry of the orifice. As the orifice diameter (d) decreases, the contraction coefficient decreases as well, resulting in a larger denominator and a smaller velocity. However, as the orifice diameter decreases, the velocity at which the flow reaches its critical velocity also decreases. This is because the smaller orifice diameter creates a higher pressure drop, which in turn increases the velocity of the fluid.

So while it may seem counterintuitive that a smaller orifice diameter would result in a smaller velocity and a smaller Mach number, it is actually the result of the critical velocity being reached at a lower velocity due to the increased pressure drop.

In summary, the likelihood of choking in a circular orifice plate is not solely dependent on the orifice diameter, but also on the density and pressure of the fluid and the geometry of the orifice. The decrease in orifice diameter may decrease the velocity, but it also affects the critical velocity and pressure drop, ultimately determining the likelihood of choking.