# Why is the pressure difference the same for B and C?

So this is the question from brilliant.org:

Which pipe (or pipes) carries water with the highest speed?

The answer given was A. I picked C, the explanation wasn't clear to me.

It says:

The pressure difference across the ends of each pipe is determined by the difference in water level between the tanks it connects. The biggest water level difference is between left and middle tanks, so water in pipe A will have the highest speed.

also

The pressure difference across both pipes is the same because the difference in water level is the same and it is smaller than the difference in levels between the left and center tanks. Therefore, the speed of the water is the same in both.

From which point are we measuring this pressure difference, it's really confusing how the explanation is given.

Just look at the height difference of the three tanks. Count the ticks.

T1 has height 4

T2 has height 8

T3 has height 6.

T2-T1 has height difference of 4, making pipe A the fastest flow rate.

T2-T3 has height difference of 2, corresponding to pipe B.

T3-T1 has height difference of 2, corresponding to pipe C.

Based on their criteria of height difference, pipes B and C have the same flow rate although in the real world the length of the pipe matters, but they are not taking that into account. The pressures are measured at each end of each pipe and are determined by the height of the tank attached to that end.

• As the pressure grows with depth in a container, the small difference in the heights of pipe connecting T1-T2 and T2-T3 should matter. Do you think that they have ignored that? Othewise the problem will become more complex. – Abhishek Anand Sep 3 at 8:06
• While the average pressure in the lower pipe will be higher, the pressure drop will still depend solely on the height difference in the tanks. – Bill Watts Sep 3 at 8:30
• Right. We are interested in the gradient only, for flow. So irrespective of where the pipe is located, flow will be the same, given viscosity is neglected. – Abhishek Anand Sep 3 at 8:35
• Just wanted to add that actually pipe A also feels pressure from reservoir T3, however T2-T3 pressure is opposite to that of T3-T1 and same in absolute value (2) , so T3 effect on pipe A can be neglected. – Agnius Vasiliauskas Sep 3 at 8:45
• What if there is also a pipe from T2 to the mid-point of the pipe? How would one make sense of it all then? – user.infamous Sep 4 at 2:20