384
12 Internal Flows in Marine Organisms
Generally, the flow in blood vessels may be laminar or turbulent, depending
on the Reynolds number, Re. As we showed in Chapter 2, in circular tubes the
critical Reynolds number is about 2000, and below this limit the influence of
viscosity dominates and stabilizes the flow so that turbulence does not occur.
However, the transition from laminar to turbulent flow in a tube may occur
at Reynolds numbers between 2000 and 12000, depending on the roughness of
the tube wall. For example, in humans the output through the cross-sectional
area of the aorta of about 4 cm 2 , is about 5 litres per minute, which gives the
mean velocity of the blood of about 21 cm/s. Therefore, the Reynolds number
will be Re rv 1500. This indicates that the flow in aorta approaches the critical
Reynolds number for turbulence.
To determine the Reynolds number of flow in the aorta of aquatic mammals,
we use the relationships given by Schmidt-Nielsen (1989):
• cross-sectional area of the aorta, in cm 2 :
A = 0.094Mo. 82 ,
(12.24)
• discharge rate in aorta (cardiac output):
Q = 187 MO. 75 ,
(12.25)
in which M is the animal mass.
Thus, the flow velocity, ii, and the Reynolds number become:
(12.26)
and
(12.27)
As flow is not at the critical level for turbulence in the circulation in humans,
it will be less so in any smaller aquatic mammals. Time is needed for some
unstable modes of motion in the flow to grow into turbulence. Due to the
pumping heart action, the blood flow in blood vessels is a pulsating flow with
velocity changing in time. Therefore, the Reynolds number will also vary in
time. We will describe briefly the propagation of pressure pulses in the blood
vessels in the next section.
12 Internal Flows in Marine Organisms
Generally, the flow in blood vessels may be laminar or turbulent, depending
on the Reynolds number, Re. As we showed in Chapter 2, in circular tubes the
critical Reynolds number is about 2000, and below this limit the influence of
viscosity dominates and stabilizes the flow so that turbulence does not occur.
However, the transition from laminar to turbulent flow in a tube may occur
at Reynolds numbers between 2000 and 12000, depending on the roughness of
the tube wall. For example, in humans the output through the cross-sectional
area of the aorta of about 4 cm 2 , is about 5 litres per minute, which gives the
mean velocity of the blood of about 21 cm/s. Therefore, the Reynolds number
will be Re rv 1500. This indicates that the flow in aorta approaches the critical
Reynolds number for turbulence.
To determine the Reynolds number of flow in the aorta of aquatic mammals,
we use the relationships given by Schmidt-Nielsen (1989):
• cross-sectional area of the aorta, in cm 2 :
A = 0.094Mo. 82 ,
(12.24)
• discharge rate in aorta (cardiac output):
Q = 187 MO. 75 ,
(12.25)
in which M is the animal mass.
Thus, the flow velocity, ii, and the Reynolds number become:
(12.26)
and
(12.27)
As flow is not at the critical level for turbulence in the circulation in humans,
it will be less so in any smaller aquatic mammals. Time is needed for some
unstable modes of motion in the flow to grow into turbulence. Due to the
pumping heart action, the blood flow in blood vessels is a pulsating flow with
velocity changing in time. Therefore, the Reynolds number will also vary in
time. We will describe briefly the propagation of pressure pulses in the blood
vessels in the next section.