Rate of change dV/dt I have the following task: "Poiscuille's Law: V=P/4Lupsilon(R^2−r^2). Assume that r is a constant as well as P,L,upsilon. Find the rate of change dV/dt in terms of R and dR/dt when L=1mm, p=100, upsilon=0.05." I cannot understand how can how can diff that, what is the t here? I can write V=500(R^2−r^2). But what after? And what is "find the rate of change in terms of...? Something like: dV/dt=dVdR/dRdt?

traquealwm

traquealwm

Answered question

2022-08-09

Rate of change d V d t
I have the following task: "Poiscuille's Law: V = P 4 L v ( R 2 r 2 ). Assume that r is a constant as well as P,L,v. Find the rate of change d V d t in terms of R and d R d t when L=1mm, p=100, v = 0.05"
I cannot understand how can how can diff that, what is the t here? I can write V = 500 ( R 2 r 2 ). But what after? And what is "find the rate of change in terms of...? Something like: d V d t = d V d R d R d t ? I am right?

Answer & Explanation

wietselau

wietselau

Beginner2022-08-10Added 28 answers

You have a function
V ( R ) = p 4 L v ( R 2 r 2 )
However, since R is a function of time, you have that.
V ( t ) = V ( R ( t ) ) = p 4 L v ( R 2 ( t ) r 2 )
So you are right, you should just use the chain rule.

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