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How high can blood really squirt from a main artery?

Now this is an old Hollywood favorite, and I need not mention the movie title Kill Bill, I thought about this for two reasons, the one being the previously mentioned movie, the other being the fact that I am an active guy and it all started when I wondered how much blood does my heart pump per second and what kind of pressure drop does it create and one thing led to another...

Being a chemical engineering student and having the mathematical capability of figuring this one out for myself I did a few calculations and got a answer, and when i tried to verify the answer somewhere on the web there where no real proof or calculations, so here is what I did.

Firstly gather some constants:

  • A good systolic heart pressure is about 100mmHg which is equivalent to 13.332 kPa
  • Then when doing some hard cardiovascular workouts a young mans heart rate cam reach 190bpm which is 3.166 bps (beats per second)
  • From a medical journal it is found that blood flow rates of 20-30 l/min is achieved while exercising, taking an average of 25 l/min which is of course 0.4166*10^-3 m^3/s
  • Diameter of an average jugular artery is roughly 8.7 mm = 0.0087m
Now for the fun part, and from first principles, from a chemical engineers point of view I thought that finding a fluid velocity firstly will be helpful, this is straight forward all I did was:

Velocity of liquid in a tube
With v the fluid velocity q the volumetric flow tempo and A the area of the artery. We already know the value of q = 0.4166*10^-3 m^3/s and A we can find by using the regular formula for the area of a circle.

Area of a circle
With D the diameter of the artery being equal to 0.0087m we find that:

That done, the initial free stream velocity can be determined as:
Now for the fun part, i.e. using your brain. I figures if you had a moving stream vertically upward battling the force of gravity, assuming you are on planet earth, then you will get a equation for the distance of vertical travel by using the following eq.
Differential equation for  distance over time
Re-arranging and integrating gives:
integration yields:
numerically plotting x over time in excel you find the following curve:
Vertical Displacement vs Time Curve

adding a trend-line  and deriving it and setting it equal to zero will give the exact time that the fluid velocity is zero, that is:
Setting the left side equal to zero the answer is t = 0.714 s using this answer and substituting it into the equations earlier derived for distance, we find after substitution that:
which is equal to:
Remember this is the answer for blood spurting out vertically, but the same can be done for a horizontal case by using projectile functions.
This was probably the most tedious way of doing this problem but at least it is a way of providing a answer to this much discussed myth on the internet.

Hope you enjoyed it and I would love to hear some comments on the method used as I am much more of a numerical guy than a algebraic kind of person.

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