Question

A blue whale’s heart pumps ∼20 liters of blood per second through its aorta, which has a diameter of 23 cm. A researcher wants to study the hydrodynamics of blood flow through the aorta. She decides to build a half-sized scale model of the aorta and flow water at room temperature through it. Calculate the flow speed in the actual aorta. What flow speed should she choose for the water in the model in order to correctly match the hydrodynamic conditions of the real aorta? Under these conditions, how does the pressure drop across the model aorta compare to the pressure drop in the real aorta? Finally, allometrically estimate the resting heart rate of the blue whale, and use it to estimate the stroke volume of the heart.

Answer 1

Generally, hydrodynamic blood flow of aorta is measured by variable diameter and wave speed in arteries. The blood flow in arteries can be measured in flow velocity V and pressure p and flow rate Q which defines as volume of fluid passing through an area during time period.

We can use Q=Av to calculate speed of blood flow in the aorta

Here v = velocity (cm/s)

Q= blood flow ( ml/s)

A= cross sectional area (cm2)

Here blue whale heart pump~20 liter of blood per second

Diameter is 23cm

So the hydrodynamic blood flow through the aorta is 2.44 cm/sec

The flow speed in arota is calculated due to presence of liquid flowing through pipe and the flow speed is 2.44 cm/ sec.

Temperature decrease, blood viscosity increase. So in blood reduce RBC and increase plasma viscosity at low temperatures.

The blue whale heart rate is 4 to 8 beats per minute , during observation showed low heart rate is 2 beats a min

Strock volume is means as amount of blood entered from ventricle with each cardiac cycle . Which is calculated by end- systolic volume and end- diastolic volume .

By using cardiac outy(CO) ~20 liter per second

Heart rate is 4-8 BPM

Strock volume (SV)=??

CO = HR × SV

SV= CO/HR

SV= 20/ 6

SV = 3.3 ml

Strock volume of heart is 3.3 ml