## DLS 2 years ago The rate of flow of a liquid through a tube of length L and radius R is V.Find the rate of flow of liquid through the combination of two tubes of same length L but radii R and R/2 when they are connected in a)Series b)parallel

1. DLS

@shubhamsrg @Yahoo!

2. DLS

2

3. shubhamsrg

What does parallel connection mean? Can you draw ?

4. DLS

5. Diwakar

The meanings of series and parallel arrangements of pipes is similar to that of electrical components.I have drawn a visual of it in the file attached. The two ends are at some pressure P. A beautiful parallel can be drawn between series and parallel arrangements of resistors and pipes. This is possible by Poisseuille's formula for rate of flow V=(pi*P*r^4)/8*n*l r is radius of cross section n is viscosity l is length of tube This can be simplified using (pi*r^4)8*n*l = C, a constant So V=CP When we draw an analogue between resistor arrangement, we can take V=some sort of current, P=some sort of potential difference and 1/C = R =resistance to the flow Although we can do the process step by step , it is easier to use the same results of resistor arrangement. Only the important thing is that volume flow (current) is same in both tubes (resistors) in series. And pressure difference (potential difference) is same across both tubes in parallel. 1) In series total resistance R=R1+R2 = (33*8*n*l)/pi*R^4 volume flow=P/R=(pi*P*R^4)/8*33*n*l = V/33 2) In parallel 1/R= 1/R1+1/R2 R=8*n*l/33*pi*R^4 You will find the flow to be 33V

6. shubhamsrg

Its gonna take me time to grasp all.

7. DLS

i got my ans and i t was easy :P that guy did it wrong

8. shubhamsrg

Please post it here, Its very rare that @Diwakar does it wrong.

9. DLS

P=P1+P2 :o

10. Diwakar

11. DLS

V/17 for series and 17V/16 for parallel

12. Diwakar

Of course, i made a grave mistake in calculations. I took 2^4=32. Sorry for that!!

13. DLS

:)