Volume Flow Rate

[TheJourney]

What is the volume flow rate of blood that moves 0.20 m/s through an artery with a diameter of 1.0 x10^-2 m/s?

A) 5.0 x 10^-6 m^3/s
B) 5 (pi) X 10^-6 m^3/s
C) (pi) x 10^-5 m^3/s
D) 2 (pi) x 10^-5 m^3/s

The correct answer is B.
Explanation: Volume flow rate is the product of blood speed and cross-sectional area: (0.20m/s)(pi/4) (1x10^-2m)^2 = 5 (pi) x 10^-6 m^3/s.

What is the generic equation for volume flow rate. I can't seem to find the equation that has pi/4. Is this a generic equation or specific for closed system vs. open systems (e.g open vs. closes pipe).

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[RocketSurgeon]

For ideal fluids:

Q = Av

Q: Volume flow rate
A: Cross-sectional area
v: Velocity

For non-ideal fluids see http://en.wikipedia.org/wiki/Hagen–Poiseuille_equation (You will probably be given this in a passage)

 

[DrknoSDN]

The pi/4 comes from converting given diameter to radius for the equation for volume of cylinder.

pi(R)^2 *Height = 1/4*pi (D)^2 * Height

[edit] Simply, R^2 always equals 1/4D^2 because your halving the diameter in two dimensions. (1/2 * 1/2 = 1/4)

 

[TheJourney]

Ohh, I get it that makes sense. Thank you!!

I was confusing the A in Q=AV for simply diameter, however it should be the area. Thus, it should be pi x r^2 and as you pointed out they converted (pi) x (radius)^2 to 1/4 (diameter)^2

Thanks again.