Biophysics problem - Pressure Change due to Plane Dive

[Red88]

Hi all,

I have been having some problems with this question from my Biophysics homework. The topic is fluid dynamics...

Homework Statement

Find the difference between the blood pressure in a pilot's head and his feet, if he sits in a plane which goes into a dive following a vertical circular path. Take the circle to have a radius of 650 meters, his speed in the circle to be 140 meters/sec and the distance from his feet to his head to be 1.30 meters.

Homework Equations

I suppose the Bernoulli equation would come into this problem since we are determining pressure change due to velocity and vertical displacement:

P1 + pgh1 + (1/2)pv1^2 = P2 + pgh2 + (1/2)pv^2, where I assumed that the density in question (p) is the same throughout and is equal to the density of air (p = 1.204 kg/m^3)

Of course, this problem could involve the concept of centripetal acceleration (a = v^2/R)...

The Attempt at a Solution

P1 + pgh1 = P2 + pgh2 + (1/2)pv^2
P1 - P2 = (1/2)pV^2 + pgh2 - pgh1
P1 - P2 = p(1/2v^2 + gh2 - gh1)
P1 - P2 = (1.204kg/m^3)((1/2)(140m/s)^2+(9.8m/s^2)(650m + 1.3m) - (9.8m/s^2)(1.30m))
=> P1-P2 = 1.95 x 10^4Pa (most likely incorrect)

Any help will be appreciated for this newbie - Thanks!

 

[stewartcs]

Is the blood density not given?

Bernoulli's equation would not really apply here since the question appears to ask for the static blood pressure differential between the feet and head (I would imagine, but don't know, that the friction and velocity head losses would be rather negligible for blood flow).

You should focus around the hydrostatic head pressure, pgh, between the head and feet.

The acceleration is the key idea here. If the blood density is given, then the pressure differential is simply pah, where p is the density, a is the acceleration (you must find it from the given data - you already listed the proper equation for finding it), and h is the height (given).

 

[Red88]

Oh ok, sounds pretty good to me! Thanks!

 

[Red88]

one more thing - should I find out the value for the density of blood (plasma)? Perhaps on an online search engine or something?

 

[stewartcs]

Typically it should be given in the problem if it is needed in order to solve the problem.

Based on your most recent question I assume it wasn't given.

There may be another approach to finding the answer than what I proposed, unless of course in Biophysics the density of blood is a common value that is widely known (other than to me!) like the value of g is.

 

[stewartcs]

Also, the answer may simply be the variable p times the numeric value of a times h.

Example: if a = 10 m/s^2 and h = 1.3 m then the differential pressure would be 13p.

 

[Red88]

cool thanks!