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Q: Poiseuille's equation shows that for laminar flow the volume flow rate through a pipe in proportional to the product of the pressure difference and the fourth power of the radius. The viscosity of water is 1.0*10^-3 Pa.s

a) Water in a pipe is flowing without turbulence under a certain pressure difference. If the radius of the pipe is reduced by 20%, what percentage increase in pressure difference is required to maintain the same flow rate?

b) In agricultural irrigation, typical values of flow velocity and pipe diameter are 1.0m/s and 100mm, respectively. Is a calculation such as in part a) applicable? (i.e. is the flow in the pipe likely to be laminar?)

I dont know how to do part a) - im guessing it involves rearranging Poiseuille's Law - but i dont know how to do the maths for it?

The Law is: J = ((pi*R^4)/(8*eta))*((delta(P))/l)

Thanks in advance!

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# Water flowing in a pipe

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