Hi, I'm attempting to do a question involving blood flowing through a blood vessel and I'm incredibly stuck and would appreciate some help. The question is as follows: 'A simplified model of blood flow through the human body makes the approximation that the flow I is proportional to the pressure differential ΔP between any two points of the system ΔP∝I. Take a length of vessel L with diameter d and viscosity η and let v(r) be the velocity as measured by r from the central axis. Assuming that the blood flow is laminar we can then model: v(r)=ΔP((d2/4)-r2)/4ηL The viscous force Fv acts on any cylindrical element due to the slow moving blood outside the element. The magnitude is given by: Fv=-ηAdv/dr where A=2πrL.' '(a) Sketch v(r) and then calculate the average velocity through the vessel' I sketched it as a negative x^2 graph except it doesn't go below the x axis. For the average velocity I integrated to find the area under the curve and then divided by the range. This gave me (ΔPd2)/(24ηL) '(b) calculate the flow through the vessel' I said that the flow = ∫v(r)2πrdr between d/2 and 0 and get the answer (ΔPπd4)/128ηL '(c) Calculate the force on the walls of the vessel' Here I was a little less sure. I worked out dv/dr to be -(ΔPr)/(2ηL) and then substituted it into the given equation to get F=ΔPπr2 and then subbed in r=d/2 (because it's the force at the wall) to get F=(ΔPπd2/4 '(d) What is the net force on the vessel? Show this is consistent with your answer to (c)' Here is where I'm completely stuck. I've tried making ΔP=dF/dA and solving differentially but I'm extremely confused. If somebody could help with this part (and correct me if I've gone wrong beforehand) then it'd be greatly appreciated. Thanks in advance.