Typical physiological conditions for blood flow in the adult human aorta are as follows:

• bulk volume flow rate: 0.067 l/s (1 l/s = 10^-3 m³/s)
• aorta diameter: 35 mm
• pulsation frequency: 7.9 rad/s (75 cycles per min)

Furthermore, blood can be roughly approximated as a Newtonian fluid with a density of 1,054 kg/m³ and a viscosity of 3.5 × 10^-3 Ns/m². Besides the Reynolds number, another important dimensionless parameter for periodic flows in pipes is the Womersley number W (or frequency parameter), defined as:

W=(D/2)(ω/ν)^0.5

where D is the pipe diameter, ν is the kinematic viscosity and ω is the pulsation frequency.

In a laboratory study through a geometrically similar model of the aorta, water is used instead of blood.
a) Determine the water bulk volume flow rate and pulsation frequency, if i) the model has the same size as the aorta, and ii) the model diameter is 2.5 times that of the aorta.
b) For the case i) above, the measured average pressure drop in water flow across the model of the aorta is Δp. Determine the coefficient by which this value should be multiplied in order to estimate the average pressure drop in blood flow across the actual aorta.

Contributed by Stavros Tavoularis, Department of Mechanical Engineering,
University of Ottawa, Ottawa, Canada. Image from UIC Biofluids Laboratory.