If someone could help with this question
Which of the following summary statements about vessel resistance is true?
A a direct relationship exists between radius and resistance
B an inverse relationship exists between radius and resistance- as vessel radius decreases resistance decreases x
C as vessel radius increases, there is a concurrent increase in resistance
D proportionally small changes in vessel radius result in relatively large changes in resistance
The relationship between resistance and radius is that as the radius of a vessel is increased, resistance decreases, thereby increasing flow. Conversely, when the radius is decreased, resistance increases, and flow is reduced. If you think about it, a narrower pipe will allow less water to be moved, while a wider pipe will allow more water to be moved. Additionally, the resistance is also inversely proportional to \(radius^4\) - i.e. \(R \propto \frac{1}{r^4}\) and therefore small changes in radius will affect the resistance greatly. (e.g. if we halve the radius (\(\frac{1}{2}^4=\frac{1}{16}\)) we will increase resistance by 16x. If we look at our answer options then:
A - I'm assuming that by direct they mean proportional, where here its inversely proportional? (incorrect)
B - for it to be an inverse relationship, as radius increases, resistance should decrease and vice versa (incorrect)
C - as vessel radius increases, resistance should decrease (incorrect)
D - Yes, as stated above, small changes in radius have large changes in resistance (correct)