A renal artery carries of a resting cardiac output of

PHYSICS · Multi-part · Fermi University Physics · Biophysics & Medical Physics · Bioelectricity, the senses and the physics of the body · Bioelectricity, the senses and the physics of the body

Life at Thermal Energy, Ch Bones, muscles, blood and body size

Problem

A renal artery carries

20\%

of a resting cardiac output of

5.0\,\mathrm{L\,min^{-1}}

. It has internal radius

2.5\,\mathrm{mm}

and length

7.0\,\mathrm{cm}

. Blood has density

\rho = 1060\,\mathrm{kg\,m^{-3}}

and viscosity

\eta = 3.5\,\mathrm{mPa\,s}

. Oxygen has diffusion coefficient

D = 2.0\times10^{-9}\,\mathrm{m^2\,s^{-1}}

in blood plasma. Plasma protein concentration is about

1.0\,\mathrm{mM}

; take

k_BT = 4.28\,\mathrm{pN\,nm}

at body temperature. ((a)) Use continuity to find the mean blood speed in this artery. ((b)) Use the Reynolds number

\mathrm{Re} = \rho v d/\eta

, with

d

the vessel diameter, to decide whether the flow in this artery is expected to be laminar or turbulent. ((c)) Using the diffusion-time estimate

t \approx L^2/2D

from Chapter 2, estimate how long oxygen would take to travel the full

7.0\,\mathrm{cm}

length of the artery by diffusion alone, and compare this with the time taken to travel the same distance at the mean speed found in part (a). What does the comparison tell you about why the body relies on bulk flow rather than diffusion over this distance? ((d)) Using the osmotic pressure relation

\Pi = ck_BT

from Chapter 3 (with

c

the number density of solute particles), estimate the osmotic pressure due to plasma proteins at

c = 1.0\,\mathrm{mM}

, expressed in mmHg (

1\,\mathrm{mmHg} = 133\,\mathrm{Pa}

), and compare it with the value of about

25\,\mathrm{mmHg}

quoted for the Starling balance at a capillary.

Browse the problem library