# Calculus 1

posted by Anonymous

The resistance of blood flow, R, in a blood vessel is dependent on the length of the blood
vessel, the radius of the blood vessel, and the viscosity of the blood. This relationship
is given by R = 8Lη/πr^4 where r is the radius, L is the length, and the positive value η is the viscosity (the larger the value of η the more viscous the blood).
(a) Find the derivative of R with respect to r. Is the derivative positive or negative? What is the physical interpretation of this? Does this result make sense?
(b) Find the derivative of R with respect to η. Is the derivative positive or negative? What is the physical interpretation of this? Does this result make sense?
(c) As body temperature increases, the blood vessel will widen (i.e. radius increases) and the blood becomes less viscous. Similarly as the body temperature lowers, the blood vessel will constrict and the blood will also become more viscous. We see then that the radius of the blood vessel and the viscosity of the blood are dependent on temperature. However, the length of the blood vessel essentially remains constant with temperature changes. Find the rate of change of resistance with respect to temperature, T. That is, find an expression for dR/dT

## Similar Questions

1. ### physics

What is the pressure gradient (the drop of pressure per length unit) in a blood vessel with a volume flow rate of ΔV/Δt = 54 cm3/s and an inner diameter of 7 mm. Hint: the viscosity coefficient of blood in the specific case …
2. ### calculus

A heart attack victim is given a blood vessel dilator to increase the radii of the blood vessels. After receiving the dilator, the radii of the affected blood vessels increase at about 1% per minute. According to Poiseulle's law, the …
3. ### physics

The drawing shows a type of flow meter that can be used to measure the speed of blood in situations when a blood vessel is sufficiently exposed (e.g., during surgery). Blood is conductive enough that it can be treated as a moving conductor. …
4. ### Physics

In the human body, blood travels faster in the largest blood vessel, the aorta than in any other blood vessel. Given an average speed of 30 cm/s, how long would it take the blood to travel 5 cm?

When blood flows along a blood vessel, the flux F (the volume of blood per unit time that flows past a given point) is proportional to the fourth power of the radius R of the blood vessel: F = kR4 (This is known as Poiseuille's Law.) …
6. ### Calculus 1

The resistance of blood flow, R, in a blood vessel is dependent on the length of the blood vessel, the radius of the blood vessel, and the viscosity of the blood. This relationship is given by R = 8Lη/πr^4 where r is the …