Water model for electric circuits: Pipe diameter?

In summary: Similarly, if you double the diameter of a pipe, its resistance to flow is cut in half.In summary, The water circuit model for electric circuits uses pressure to represent electric potential and flow rate to represent electric current. The pipe diameter in the water model can be varied, but since water is incompressible, the flow rate remains constant. In an electrical analog, the diameter of the conductor would correspond to resistance, and increasing the diameter would decrease the resistance. However, the pipe-circuit analogy is not perfect and has limitations. A more accurate analog would be flow through a porous medium, where the permeability of the medium and viscosity of the water play a role in the equation. Overall, while the analogy can be helpful in understanding certain concepts,
  • #1
greypilgrim
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Hi.

There's this nice water circuit model for electric circuits where pressure corresponds to electric potential and the (mass or volume) flow rate to electric current.

In the water model, we can vary the pipe diameter along the circuit. Since water is practically incompressible, the flow rate remains constant, i.e. the flow velocity must increase when the pipe diameter decreases.

Is there an electrical analog to the pipe diameter? It certainly does not correspond to a resistance, since no energy is dissipated if we assume frictionless flow.

Also, which pressure is the closest analog to electric potential? I guess it must be total pressure, since it should be the same at two points of different pipe diameter (if there's no dissipative element between them) to correctly model zero voltage drop along perfect conductors, and static and dynamic pressure would not be constant individually when the flow velocity changes.
 
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  • #2
greypilgrim said:
Is there an electrical analog to the pipe diameter?
The obvious equivalent is the diameter of the conductor, which does effectively change the resistance, especially if it is too small relative to the amount of current. Assuming frictionless flow is equivalent to assuming a superconductor.
 
  • #3
greypilgrim said:
Is there an electrical analog to the pipe diameter? It certainly does not correspond to a resistance,
In the analogy the diameter would be one of the factors that determines resistance. Specifically, the resistance of the pipe varies as 1/r^4.

https://en.m.wikipedia.org/wiki/Hagen–Poiseuille_equation

Note, the pipe-circuit analogy is actually fairly poor for a lot of reasons. The biggest problem is that fluid flow in a pipe is horrendously complicated, far more complicated than the electrical circuit laws. So the analogy should only be taken very qualitatively. Asking for quantitative details like that quickly exposes this prime weakness in the analogy.
 
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  • #4
A more accurate quantitative analog between water flow and electrical current flow would be flow through a porous medium. In such a case, for the porous medium, the equation would be $$\vec{v}=-\frac{k}{\mu}\nabla P$$where ##\vec{v}## is the superficial water velocity, k is the permeability of the porous medium, and ##\mu## is the viscosity of the water. The corresponding equation for current flow would be $$\vec{j}=-\frac{1}{r}\nabla V$$where V is the electrical potential, r is the resistivity of the conductor, and ##\vec{j}## is the current density.
 
  • #5
greypilgrim said:
Is there an electrical analog to the pipe diameter? It certainly does not correspond to a resistance, since no energy is dissipated if we assume frictionless flow.
The electrical analog would be resistance. If you double the cross sectional area of a conductor, its resistance is cut in half.
 

FAQ: Water model for electric circuits: Pipe diameter?

1. What is the significance of pipe diameter in the water model for electric circuits?

The pipe diameter in the water model for electric circuits represents the cross-sectional area of the wire or conductor in an electric circuit. It determines the flow rate of water (electric current) through the circuit and the resistance to that flow.

2. How does changing the pipe diameter affect the flow of water in the electric circuit?

A larger pipe diameter allows for a higher flow rate of water, representing a lower resistance in the electric circuit. Conversely, a smaller pipe diameter results in a lower flow rate and a higher resistance in the circuit.

3. Is there an optimal pipe diameter for efficient flow in an electric circuit?

Yes, there is an optimal pipe diameter for efficient flow in an electric circuit. This is determined by the overall design and components of the circuit, as well as the properties of the material used for the wire or conductor.

4. Can the pipe diameter be adjusted to control the flow of water in an electric circuit?

Yes, the pipe diameter can be adjusted to control the flow of water in an electric circuit. This is commonly done by using different sizes of wire or conductors in the circuit, or by adding resistors or other components to alter the flow rate.

5. How does the water model for electric circuits relate to real-life electrical systems?

The water model for electric circuits is a simplified representation of how electricity flows through a circuit. It helps to visualize and understand concepts such as resistance, voltage, and current. While it is not an exact representation of real-life electrical systems, many of the principles and equations used in the water model can be applied to analyze and design real circuits.

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