Velocity through a pipe... <arg>

[Mouse51180]

A pump operates normally at 675gpm through a 7.25" ID pipe. What is the velocity of the water (ft/s) as it travels through the pipe?

Velocity = Flow / Area of a Pipe

Flow = 675gpm converted to gps = 675 / 60 = 11.25gps

Area of a pipe = πr²
π = 3.14
r = 7.25" / 2 = 3.625"

3.14 * 3.625π = 41.26" convert to ft = 41.26 / 12 = 3.44ft.

Velocity = 11.25 / 3.44 = 3.3ft/s

My answer is 3.3ft/s
Correct Answer is 5.3ft/s

What am I doing wrong?

 

[DrPhil]

A pump operates normally at 675gpm through a 7.25" ID pipe. What is the velocity of the water (ft/s) as it travels through the pipe?

Velocity = Flow / Area of a Pipe

Flow = 675gpm converted to gps = 675 / 60 = 11.25gps

Area of a pipe = πr²
π = 3.14
r = 7.25" / 2 = 3.625"

3.14 * 3.625π = 41.26" convert to ft = 41.26 / 12 = 3.44ft.

Velocity = 11.25 / 3.44 = 3.3ft/s

My answer is 3.3ft/s
Correct Answer is 5.3ft/s

What am I doing wrong?

Thank you for identifying the units for the numbers. The next step that will help keep you honest is to include the units for EVERY number you write down. Lets start with
....11.25 gps -- that's good. [or the units could be written gal/s]

The trouble begins with Area. The arithmetic you did resulted in units of ft -- but an area should be ft^2. You needed to convert r to feet, and then to square it:

....Area = pi r^2 = 3.14*(3.625"/12("/ft))^2 = 0.287 ft^2

Now when you wrote the velocity, you used 11.25 BUT you didn't write the units (gal/s).
You need to convert gallons to cubic feet! I find that a U.S. liquid gallon is 231 in.^3.

Follow the units, and do the same operations on the units as on the numbers. If you wind up with ft/s, that will be the answer.

 

[Mouse51180]

Got it now...was squaring π when just needed to square my radius.

I also found that I didnt need to convert the gpm to gps. Looking back over my given formulas I am given the formula cfs = gpm / (7.48 * 60).

So my flow is figured out by
cubic feet per sec. = 675gpm / (7.48 * 60)
cfs = 675gpm / 448.8
cfs = 1.5

area = 0.287 ft.sq.

Velocity = 1.5cfs / 0.287ft.sq.
Velocity = 5.24ft/s

Thanks for your help.