Question 9

[tnfifn3735]

How can the equation be used when we don't know what L and Radius are?

[jellywing_2058]

The question clearly says “the blood vessel is of unit radius”; however you might wonder about the units, which is to say whether it is 1 m, or 1 cm or in any other unit.

Looking at the rest of the quantities it is quite clear that it ought to be 1 cm, which would be consistent with the cgs system of units. As we can see, the question is in the centimeter gram second system (cgs) since they are using cm, s and dyn, which are the cgs units.

Further, a force of 1 dyn is defined as the force required to accelerate a 1 g mass by 1 cm/ s^2. We must therefore take our r = 1 cm.
Also, little common sense says a blood vessel cannot be as huge as 1 m.

We also will put L = 1 cm, as the question wants us to find out “the pressure drop per cm of the blood in the first blood vessel”.
Therefore, the Pressure drop 1 cm down the blood flow, so L = 1 cm.

Plugging:

R = 1 cm,
L = 1 cm,
V/ t = 80 cm^3/ s – The Volume flow rate when the body is at rest, and

n = 0.04 dyn s/ cm^3,

we get our ΔP – the Pressure drop as:
ΔP = n 8 VL/(ΠR^4t)
ΔP = n 8(V/t)L/(ΠR4)
ΔP = (0.04 dyn s/cm^3)( 8 )(80 cm^3/s)(1 cm)/(1 cm^4 Π)
ΔP = 25.6/Π dyn/cm^3