An artery branches into two smaller, identical arteries as shown in the diagram.

Question

An artery branches into two smaller, identical arteries as shown in the diagram. The largest
artery has a diameter of 10 mm. The two branches have the same diameter = 5 mm. The average speed of the blood in the main artery is given in the diagram. The blood has a density of 1004 kg/m^3
-Calculate the volume flow rate through the main artery in SI units (m^3/s)
-Now convert the flow rate into the units usually used in clinical applications, liters/minute.
-Calculate v, the average blood flow speed in the two branches of smaller radius.

Explanation / Answer

Diagram is not given. So let average speed of the blood in the main artery = x m/sec

Volume flow rate through the main artery = VA = x**0.25*100*10-6 m2 = 7.854 * x * 10-5 m3/sec

In litres/minute we get, Volume flow rate = 7.854 * x * 10-5 * 103/(1/60) Litres/min = 4.7124 * x Litres/min

A1V1 = 2A2V2

=>D12x = 2D22v

=>v = 100x/(2*25) = 100x/50 = 2x m/sec.

You can substitute the value of x from the diagram to get the results.

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