# Good analogy for watts vs amps?

According to plumbing analogy I've hard time seeing why power is measured in volts*amps, instead of just amps.

I found an analogy from http://science.howstuffworks.com/environmental/energy/question501.htm

Electrical power is measured in watts. In an electrical system power (P) is equal to the voltage multiplied by the current.

The water analogy still applies. Take a hose and point it at a waterwheel like the ones that were used to turn grinding stones in watermills. You can increase the power generated by the waterwheel in two ways. If you increase the pressure of the water coming out of the hose, it hits the waterwheel with a lot more force and the wheel turns faster, generating more power. If you increase the flow rate, the waterwheel turns faster because of the weight of the extra water hitting it.

This explanation contrasts two ways of increasing the power:

1. increasing the pressure [volts] or
2. increasing the flow rate [amps].

But increasing the pressure also increases the flow rate!? What am I missing here?

Would it be more precise to say that I can increase the power by:

1. increasing the pressure [volts] while keeping flow rate [amps] the same (by using hose with smaller diameter [increasing resistance]) or
2. increasing the flow rate [amps] while keeping the pressure [volts] the same (by using hose with bigger diameter [decreasing resistance]?

Does increasing water pressure while reducing hose diameter (so that flow rate stays the same) really give you more powerful waterwheel?

• Increasing the pressure (voltage) with the same pipe (resistance) does increase the current in both analogies - so increases the power as V^2. You are on roughly the right lines - if you increase voltage and want to keep the current constant you have to increase resistance too. (In a hydro power system you wouldn't use a smaller pipe - that wastes energy - but you'd use a smaller nozzle - ever put your finger across a hosepipe? you reduce the flow rate but its actual velocity and force are much greater. Try it on the cold tap now.)
– user16324
Commented Oct 8, 2016 at 22:30
• Not a full answer, but to "why power is measured in volts*amps", look at the units: $V = J/C$, $A = C/s$, $W = J/s = J/C \times C/s = V \times A \rightarrow P = I\times V$. Power is the amount of charge flowing per second (current) times the amount of energy carried by that charge (voltage). Commented Oct 8, 2016 at 23:26

The water analogy is full of leaks. A better analogy, if you need one, is a closed circuit water pumping system such as a central heating hot-water system. Pump = battery, pressure = voltage, radiators = resistors, current = current.

Forget all that for a moment: why does voltage affect power? Increasing the voltage allows us to get the same current through a higher resistance. Since more work is required to do this then the power must be increasing.

• my air tank doesn't leak (much) , but don't ask me to explain it in layman's terms ;) Commented Oct 8, 2016 at 23:41
• "Water analogies full of leaks". I see what you did here... and I also agree. Moreover, volts and amps always had more significance to me than pressure and flow, so I don't think analogies are always worth elaborating.
– dim
Commented Oct 9, 2016 at 6:09

For a simple water analogy, if you double the pressure, the flow rate will double. This is based on the fluid "load" being equivalent to an electrical resistor.

So you've doubled pressure and accordingly, the flow rate has doubled and, this naturally and mathematically means the power imparted to the load has risen 4 times.

Nothing wrong with that analogy at all.

If you double the voltage across a resistor, power increases 4 times. Maybe you've seen the formula power = volts squared divided by resistance. The squaring term accounts for the current doubling when you double the voltage.

I recently plotted the energy in a screw air compressor ( 3 phase) and thought I would share for you.

Compare the cumulative air flow (at some nozzle velocity) in CFM and the electrical energy consumed in kWh

They are identical.

So power, P=IV times time is Energy is equivalent to cumulative volume of air mass at a fairly constant velocity. (regulated by pressure and nozzle size)

Orange is CFM and light blue is kCFM-cum. BLUE is kWh and thin blue is PSI air pressure in the tank.