Note: My question is duplicate of Why doesn't water come out of tap/faucet at high pressure when I turn it on?. None of the answers given there explains how the continuity equation fits properly. That's why I am asking this question.
I do not understand the Hydraulic analogy explained on wikipedea.
I asked my Network analysis teacher for an explanation .
He told me that cross-section area of a pipe represents its resistance and flow of water represents current passing through that pipe. Like in a tap when we change the area of aperture the flow rate of water changes, this is analogous to change in current in a wire due to the change cross-section area of the wire.
There is a contradiction in my understanding.
Contradiction: When we decrease the area of the mouth of the tap by our thumb the amount of water flowing out remains same but if we decrease the area of aperture of the tap by turning the knob the amount of water flowing out decreases.why?
Is it due to the change in type of flow i.e the flow changes from laminar to turbulent or choked?
I found a flaw by applying equation of continuity as:
Suppose two parallel resisters are connected to voltage source as shown:
Let's name the three wires as pipe-0(having the battery) ,pipe-1(having resister $R_1$) and pipe 2(having resister $R_2$).
All three pipes are of same length. Resistances of different wires are equivalent to the respective aperture radius of different pipes.
Our analogy is to interchange the terms current $i=dq/dt$ (amount of charge crossed in a unit time) with flow rate of water i.e $i \equiv dm/dt$ (amount of mass of water crossed in unit time).
Let's remove the wire having $R_2$.
The current $I$ in pipe 0 will decrease as the resistance of circuit increase.
removing the resistance is analogous to change the area of pipe-2 to $0$. On the other hand removing pipe 2 will not change water flow $dm/dt$ in pipe-0 because of Equation of Continuity.
I wrote my understanding about the situation to tell the community that my question is not Home-work like
In essence my question is
1.How the tap works? And how can we apply the equation of continuity to the water flow when we turn the knob and when we cover the tap with thumb?
2. Where I'm getting wrong with my understanding of the Hydraulic analogy.