Question

Water flows through a horizontal pipe similar to the pipe in DL. It enters the pipe at point (1), then leaves the pipe at point (2), which is open to the atmosphere. The height of the water in each vertical column is below. Now suppose that the length of this pipe is doubled. The pressure at point (I) is the same as before. Point (2) is still open to the atmosphere. Water is again allowed to flow from point (1) to point (2). Assume resistance changes linearly with pipe length. 2) open to air open to air 2 2 a) How does the resistance of the longer pipe compare to that of the shorter one? (Think b) Compare the flow rates in the two pipes. If they are different, by how much? Explain e) Fill in the water levels in each of the vertical columns in the pips whose length has in terms of thermal energy and friction.) your answer and show your reasoning. been doubled, in the diagram below. Be clear and accurate in drawing each water level

Answer 1

1. As we increase the pipe length, its resistance increases linearly. So, its resistance gets doubled when we double the length of pipe.

2.Flow rate = delta p/resistance ,

So, as compared to case-1, in case-2 resiatnce gets doubled but delta p remains same. So, flow rate gets half as compared to case-1.

c. In second figure, pressure drop upto 2nd verticle column = $RXL/2$ where R = DP/2L is pressure drop per unit length, pressure drop per unit length is same for both the cases, in first pipe at 2nd verticle column, pressure drop is R1XL/2, R1 = DP/L

So, pressure drop in 2nd pipe = DP/4

And pressure drop in 1st pipe = DP/2

So, pressure drop in 2nd pipe is half as compared to 1st pipe for the same location. And pressure drop in 1st case in 3 , so in 2nd case it will be 1.5 ,So length of water in the 2nd verticle column =6- 1.5 = 4.5 bars

Similarily in third column height will be = 6 - 6/2 = 3 bars