How Does Changing Pipe Radius Affect Pressure in Laminar Flow?

[ussrasu]

I need some help with this question.

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 don't know how to do part a) - I am guessing it involves rearranging Poiseuille's Law - but i don't know how to do the maths for it?

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

Thanks in advance!

 

[OlderDan]

I don't know how to do part a) - I am guessing it involves rearranging Poiseuille's Law - but i don't know how to do the maths for it?

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

Sounds to me like you are supposed to assume all else stays the same except radius and pressure. Write your J equation for two different combinations of radius and pressure difference and set the equations equal. You can solve for the ratio of pressure differences in terms of the known ratio of radii.

 

[ussrasu]

So i let R = 0.8 on one side, and the final pressure as what I am trying to find, and then on the other side i let R=1 as that's at the initial radius, and let the pressure equal 1 here asell and then solve for Final Pressure?

Thanks!

 

[OlderDan]

So i let R = 0.8 on one side, and the final pressure as what I am trying to find, and then on the other side i let R=1 as that's at the initial radius, and let the pressure equal 1 here asell and then solve for Final Pressure?

Thanks!

That's the idea, but you don't have to use 1 for anything. You can use ratios. For one case you have R1 and deltaP1; for the second case you have R2 and deltaP2. When you set the two equal you can rearrange the equation to solve for the ratio deltaP2/deltaP1 in terms of the known ratio R2/R1.

 

[ussrasu]

Cool thanks!

 

[ussrasu]

Does anyone have any ideas on how to explain part b to this question? What would you say?

Thanks

 

[FredGarvin]

Calculate the Reynolds number for that flow. If it is <3500 or so, it will be laminar.