Question

The mean velocity in an artery of internal diameter 2.5 mm is 0.25 m/s. Assuming that blood has a viscosity of 0.004 Pa.s and a density of 1000 kg m⁻³.

a) Determine: i. whether the flow is laminar or turbulent ii. the volume flow rate through the artery

b) Assume that the diameter of this blood vessel above is doubled, what would happen to the total volumetric flow rate? Explain your response.

c) What would happen in terms of type of flow, velocity and pressure, if this artery was obstructed

Answer 1

a) (i) If Reynolds no less than 2000 ..flow is laminar and if Reynolds no greater than 3000 it is said to be turbulent.

The Reynolds number (Re) of a flowing fluid is calculated by multiplying the fluid velocity by the internal pipe diameter (to obtain the inertia force of the fluid) and then dividing the result by the kinematic viscosity (viscous force per unit length).

So Re = (0.25 m/s * 2.5 mm) / 0.004 Pa.s= 156.25

So the flow is laminar.

(ii)formula for the volume flow rate Q = A v

A = area of circle = 3.14 * 1.25 *1.25 = 5 mm^3/ s

b) When the diameter is doubled the radius doubles so since area is radius square the area becomes 4 times that of initial area.So volume flow rate becomes 4 times that of initial.

c)When the artery gets blocked the flow rate decreases and becomes .When the flow rate becomes 0 velocity becomes 0Then pressure on the artery walls increases.

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