Calculating the Constant for Measuring Flow Rates in Open Channels

[Frustra8ed]

I'm having trouble a problem and I was hoping someone could show me some direction.

Q:
A weir is used to measure flow rates in open channels. For a rectangular weir the expression can be written as Q=288.8 LH^(3/2).
Where Q= discharge rate, in gal/h
L= Length of weir opening parallel to liquid, in inches
H= height of fluid above crest, in inches

As the channels become larger, the weir opening can be expressed as follows:
Q in cubic feet per second, with L and H in feet.

Determine the new constant.

The answer is 5.35, and I can't figure out how they derived it. I think it has to do with converting units, but I don't know.

Any help is appreciated.

Thanks,

Frustra8ed

 

[Justin Lazear]

You're right, it's all about the units.

You have Q, which is initially in gal/hour, and you want to get it into ft^3/second. How would you do this?

You have L, which is initially in inches, and you want to get it into feet.

W is like L.

--J

 

[FredGarvin]

You have the right idea. Set up the same equation but add the units conversions on the appropriate sides:

One side will be the conversion from gal/hr to ft^3/sec. The other side will be the unknown times the two conversions from ft to in. Don't forget that one of those connversions is to a power. Solve for the unknown.

That being said, I went through this problem 4 times and I keep getting the answer, except a factor of 10 off. I keep getting 53.9. Maybe someone else can verify that.

 

[Justin Lazear]

I'm getting 5.35.

The easier way to do this problem is to figure out the units of the constant 288.8, and then convert these units into the units of the 5.35 constant.

The 288.8 constant has units gal/hr/in^(5/2). The desired units are ft^.5/s.

--J

 

[Frustra8ed]

Thanks!
I was on the right track, just needed a boost. I appreciate the help.

Frustra8ed