question about orifices and tank draining

[engineer123]

Hi All,

I'm trying to solve this problem about a tank draining:

A 3 inch diameter orifice on the side of a 5 ft diameter tank draws the surface down from 7 ft to 5 ft above the orifice in 53 seconds. Calculate the discharge coefficient. 

I started using the equation Q = C A sqrt 2gh, but the solution manual shows a different equation using time. I don't see that equation anywhere in the PE formula handbook and don't know how I could even derive that! so I'm wondering is there another way I can solve this? 

If anyone can please explain, please let me know! Thanks (p.s. the answer is supposed to be C = 0.77)

 

[Slay the P.E.]

Hi All,

I'm trying to solve this problem about a tank draining:

A 3 inch diameter orifice on the side of a 5 ft diameter tank draws the surface down from 7 ft to 5 ft above the orifice in 53 seconds. Calculate the discharge coefficient. 

I started using the equation Q = C A sqrt 2gh, but the solution manual shows a different equation using time. I don't see that equation anywhere in the PE formula handbook and don't know how I could even derive that! so I'm wondering is there another way I can solve this? 

If anyone can please explain, please let me know! Thanks (p.s. the answer is supposed to be C = 0.77)

View attachment 12603

The equation you attempted to use is for steady state, which is achieved only when:

1. the fluid being drained is replenished at the same rate at which it is leaving through the orifice, or
   
2. the volume of fluid in the tank is so large that one assumes the water level remains constant during the period of interest.
   

Neither one of the above apply for the problem you posted. In that problem, you have a transient effect, and there is no other way to solve it other than considering time-dependent effects.

The equation they used in the solution is derived in page 17-19 of the MERM13 and it is equation 17.83. It is a time-dependent solution.

 

[engineer123]

The equation you attempted to use is for steady state, which is achieved only when:

1. the fluid being drained is replenished at the same rate at which it is leaving through the orifice, or
   
2. the volume of fluid in the tank is so large that one assumes the water level remains constant during the period of interest.
   

Neither one of the above apply for the problem you posted. In that problem, you have a transient effect, and there is no other way to solve it other than considering time-dependent effects.

The equation they used in the solution is derived in page 17-19 of the MERM13 and it is equation 17.83. It is a time-dependent solution.

@Slay the P.E. I don't have that reference but do you mind posting the equation 17.83? thanks for your help!

 

[Slay the P.E.]

It's exactly the same one you posted from the solution in your book. The one with the difference of the square roots of the heights.

 

[Audi Driver P.E.]

@Slay the P.E. I don't have that reference but do you mind posting the equation 17.83? thanks for your help!

You don't have the MERM???? Why not?

 

[Slay the P.E.]

You don't have the MERM???? Why not?

They're taking Environmental Engineering exam, per their profile.

 

[Ramnares P.E.]

Enviro's sneaking into the Mechanical board for advice, what gives??!

 

[Audi Driver P.E.]

They're taking Environmental Engineering exam, per their profile.

Whoah. Missed that. Seems an oddly appropriate place to ask the question, I guess.