# calculus

posted by .

for a given patient it is determined that the blood vessel may rupture if its diameter increases faster than 200 um/s. The blood vessel starts with diameter 4mm and needs to expand to a diameter of 7mm. Is it safe to inflate the balloon at a constant rate of 30 mm^3/s? What about 60 mm^3/s.?

• calculus -

From the previous post, keeping all the measurements in mm,

dV/dt = (4πr^2 + 60π) dr/dt

so, if dV/dt = 30,

30 = 4π(16 + 15) dr/dt
so
dr/dt = .0770 mm/s = 77 um/s. That means that the diameter is increasing by 154um/s, so that's ok. As the diameter increases, the rate of expansion slows down.

At 60mm^3/s, the inflation rate starts at 308um/s. Boom!

## 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

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. …
5. ### 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?
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 …
7. ### 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 …

Need help on this problem please! Been stuck for half hour trying to figure it out but I can't get through a. A and B look to be similar but I don't know how to do them! Please help! ----------------------------------- The resistance …
9. ### Math

The blood vascular system consists of blood vessels (arteries, arterioles, capillaries, and veins) that convey blood from the heart to the organs and back to the heart. This system should work so as to minimize the energy expended …
10. ### Math

The blood vascular system consists of blood vessels (arteries, arterioles, capillaries, and veins) that convey blood from the heart to the organs and back to the heart. This system should work so as to minimize the energy expended …

More Similar Questions