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:
(source: tutorvista.com)
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.
Best Answer
The tap works by changing the minimum cross-sectional area of the flow. For a given pressure difference (upstream pressure minus downstream pressure) flow rate is a function of minimum cross-sectional area. Using your thumb would do the same thing. You can stop the flow with your thumb if you are strong relative to the force of the flow.
http://people.uncw.edu/lugo/MCP/DIFF_EQ/deproj/orifice/orifice.htm
Probably you are misunderstanding the Equation of Continuity. The Equation of Continuity only means that the mass flow rate in equals the mass flow rate out. It does not mean that the flow in and the flow out never change. Flow rate in and flow rate out can change simultanteously. Your statement "On the other hand removing pipe 2 will not change water flow [rate]" is incorrect. Removing pipe 2 will make a big difference in total flow if it is large in cross section compare to pipe 1. It will make a small difference in total flow if it is small in cross section compare to pipe 1. Your statement "When we decrease the area of the mouth of tap by our thumb the amount of water flowing out remains same" is also incorrect. Instead, the flow rate approaches zero as you make the cross-sectional area of the unblocked portion of the mouth small.