Impact of a Fluid Jet Experiment

[SherlockOhms]

Homework Statement

We recently did an experiment involving the impact of fluid jet on both plane and cupped surfaces. See the diagram attached for the experimental set up. We were asked to 1) verify the conservation of momentum and 2) calculate the discharge coefficient of the nozzle from which the jet emanates.

As you can sort of make out from the diagram below, a jockey mass was placed on a lever arm which was then balanced by the exerted force on the plate below due to the fluid jet. The Force exerted by the fluid can then be found by allowing the moment of the jet's force equal to the moment of the jockey masses weigh about the turning point. Then, you can prove the conservation of momentum by seeing if this value of F equals $\rho Qv_1$ where $\rho$ is the density of water, $Q$ the flow rate and $v_1$ the velocity of the jet leaving the nozzle. $Q$ was calculated an thus the value of $v_1$ could be calculated using the continuity equation and the area of the nozzle. This value was given and the distances from the turning point were measured for each jockey mass applied to balance the various different flow rates. Right so far?

My problem is that I have no clue how to calculate the value of $C_D$ for the nozzle. On our handout it says to use the equation $C_D = C_V \times C_C$ but I have absolutely no idea what $C_V$ and $C_C$ stand for let alone how to find them. Could somebody point me in the right direction?

Homework Equations

$Q = Av$
$F_{Rx} = \rho Q(V_2cos\theta - V1)$

The Attempt at a Solution

Sort of outlined what I've done above.

 

[SteamKing]

You only show the first page of the handout. Are there any other pages? Are you sure you haven't come across Cc and Cv before? Have you done any research?

 

[SherlockOhms]

You only show the first page of the handout. Are there any other pages? Are you sure you haven't come across Cc and Cv before? Have you done any research?

That isn't the first page of the handout which we were given. I only posted that to show the equipment set up. I'll post all the pages of our actual handout (there's no reference to $C_V$ or $C_C$ anywhere). No, we've never come across these coefficients in class. I looked up $C_V$ and found that it to be the velocity coefficient. How do I calculate this? I'm yet to find anything on $C_C$.

 

[SherlockOhms]

 

[SherlockOhms]

That's every page.

 

[haruspex]

That isn't the first page of the handout which we were given. I only posted that to show the equipment set up. I'll post all the pages of our actual handout (there's no reference to $C_V$ or $C_C$ anywhere). No, we've never come across these coefficients in class. I looked up $C_V$ and found that it to be the velocity coefficient. How do I calculate this? I'm yet to find anything on $C_C$.

C_C is the contraction coefficient. It represents how much smaller the effective area of the nozzle is than the measured area. It depends on the shape of the nozzle cross section, turbulence, and shape/tapering of the approach to the nozzle. (See Borda mouthpiece.) I don't know that C_C is a standard symbol for it. http://nal-ir.nal.res.in/3759/1/performance_of_clonical.pdf uses CA.

I have not studied the pages you posted (hardly my area of expertise), so I am not certain that you actually need to use the equation that involves C_C, but since it is mentioned, I guess you probably do.

 

[SherlockOhms]

C_C is the contraction coefficient. It represents how much smaller the effective area of the nozzle is than the measured area. It depends on the shape of the nozzle cross section, turbulence, and shape/tapering of the approach to the nozzle. (See Borda mouthpiece.) I don't know that C_C is a standard symbol for it. http://nal-ir.nal.res.in/3759/1/performance_of_clonical.pdf uses CA.

I have not studied the pages you posted (hardly my area of expertise), so I am not certain that you actually need to use the equation that involves C_C, but since it is mentioned, I guess you probably do.

Thanks for that. I actually found something in my notes stating that the value of $C_C$ for a nozzle is approximately 1. Is this correct? If so, how would I go about calculating $C_V$?

 

[haruspex]

Thanks for that. I actually found something in my notes stating that the value of $C_C$ for a nozzle is approximately 1. Is this correct? If so, how would I go about calculating $C_V$?

My (shaky) understanding is that it works the other way around: you determine the discharge coefficient and contraction coefficient by experiment, and deduce the velocity coefficient from the formula. This is why I suspect you don't need the formula at all for the purpose of this question - you are not asked to find C_C or C_V.
This link might help: http://www.codecogs.com/library/eng...s/pipes/head_loss/nozzles-and-mouthpieces.php.
The awkward part, it seems to me, is that the question asks:

1) verify the conservation of momentum and 2) calculate the discharge coefficient

You can't do (1) without first solving (2), and to solve (2) you need to assume (1). The only way I see around it is to have some independent measurement of the flow rate and flow velocity, but if you didn't take such measurements at the time you're a bit stuffed.

 

[SherlockOhms]

My (shaky) understanding is that it works the other way around: you determine the discharge coefficient and contraction coefficient by experiment, and deduce the velocity coefficient from the formula. This is why I suspect you don't need the formula at all for the purpose of this question - you are not asked to find C_C or C_V.

This link might help: http://www.codecogs.com/library/eng...s/pipes/head_loss/nozzles-and-mouthpieces.php.

The awkward part, it seems to me, is that the question asks:
You can't do (1) without first solving (2), and to solve (2) you need to assume (1). The only way I see around it is to have some independent measurement of the flow rate and flow velocity, but if you didn't take such measurements at the time you're a bit stuffed.

Well, we did take measurements of Q throughout the experiment but that was about it. The first question, verifying the conservation of momentum just seemed to be calculating the Force on the plate via the moment balance and then seeing if this matched $$F = \rho Q (V_1 - V_2cos\theta)$$
Where $Q$ is the measured flow rate and $V_1$ can be found using the continuum equation and some simple kinematics. That was my understanding of proving conservation of momentum.

 

[haruspex]

$V_1$ can be found using the continuum equation and some simple kinematics.

But see the link I posted, http://www.codecogs.com/library/eng...s/pipes/head_loss/nozzles-and-mouthpieces.php. The velocity coefficient is the ratio between the theoretical velocity and the actual velocity. Sounds like you're assuming that coefficient is 1. To find a value for it you would need a direct measurement of the velocity.