I don\'t understand how to solve this question can someone please provide me wit

Question

I don't understand how to solve this question can someone please provide me with a step by step solution

P4.6 Say that the water pump shown in E4.9 generates 12 bar of pressure at its output,
and the pressure at the pump’s input is 1 bar. The resistor part of the pipe has
resistance equal to 1.2 bar · (sec/l). Assume there is zero resistance in the parts
of the pipe containing no obstructions.

(a) Without the small holes present, what is the current?

(b) Assuming the holes are small enough not to change the pressure and flow in the pipe, find the pressure at the location of the middle hole. Hint: Consider the resistor region to be separated into two distinct resistor regions, one on either side of the middle hole. Their resistances are 0.3 bar · (sec/l) and 0.9 bar · (sec/l). The currents through each resistor region are the same as that determined in (a).

Explanation / Answer

(a) Pressure at output of pump = 12 bar

Pressure at input of pump = 1 bar

Pressure difference = Pressure at output - Pressure at input = 12 bar - 1 bar = 11 bar

Resistance = 1.2 bar (sec/l)

Current = Pressure difference/ Resistance = 11 bar/ 1.2 bar (sec/l) = 9.167 l/sec

(b) The resistor region is separated into two distinct resistor regions, one on either side of the middle hole. Their resistances are 0.3 bar (sec/l) and 0.9 bar (sec/l).

Current through both resistors is same.

Let pressure at middle hole is P

Current through 0.3 bar (sec/l) resistor = Pressure difference/ Resistance = (12 - P)/0.3

Current through 0.9 bar (sec/l) resistor = Pressure difference/ Resistance = (P - 1)/0.9

Since current through both resistors is same,

(12 - P)/0.3 = (P - 1)/0.9

P = 9.25 bar

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