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July 30, 2014

Posted by **Angie** on Tuesday, September 4, 2012 at 3:10pm.

A commonly used rule of thumb is that average velocity in a pipe should be about 1 m/s or less for "thin" (viscosity about water). If a pipe needs to deliver 6,000m^3 of water a day, what diameter is required. My teacher added flow area multiplied by the velocity equals the volumetric flow rate. The answer should be in cm.

- Chemistry/Math -
**Steve**, Tuesday, September 4, 2012 at 3:23pmif the diameter is d meters, the cross-section of the pipe has area pi/4 d^2 m^2

In one second, at 1 m/s, then, pi/4 d^2 m^3/s of water will flow through the pipe

now just plug in the numbers:

6000m^3/day * 1day/86400s = pi/4 d^2 m^3/s

d = 1/3 √(5/2pi) = 0.297m

- Chemistry/Math -
**Angie**, Tuesday, September 4, 2012 at 3:30pmWhen I calculate what you did, I don't get the same answer.

- Chemistry/Math -
**Steve**, Tuesday, September 4, 2012 at 3:33pmwell, I may have botched it. What calculations do you have?

- Chemistry/Math -
**Angie**, Tuesday, September 4, 2012 at 3:35pm(6000)(1/86400)*(1/3)sqrt(5/2Pi)

- Chemistry/Math -
**Steve**, Tuesday, September 4, 2012 at 3:45pmyou did not read carefully above: if you solve for d in the equation

6000m^3/day * 1day/86400s = pi/4 d^2 m^3/s

you get (ignoring the units)

6000/86400 = pi/4 d^2

d^2 = 5/(18pi)

Hmmm. I did have a typo above, but I still get

d = .297m = 29.7cm

- Chemistry/Math -
**Angie**, Tuesday, September 4, 2012 at 3:56pmWhere does the 5 come from?

- Chemistry/Math -
**Steve**, Tuesday, September 4, 2012 at 4:23pm6000/86400 = 60/864 = 5/72

5/72 = pi/4 d^2

d^2 = 5/72 * 4/pi = 5/(18pi)

forget your algebra skills?

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