When the shower is running and someone flushes a toilet, why does the shower get cold (or sometimes hot) in some houses, but not others?
More importantly, would fixing that require replacing the water heater, or re-doing the piping in the entire house? Or is there some cheap/easy way to fix it?
One of the most common plumbing configurations, is a trunk and branch system. This is where a larger diameter pipe runs from one end of the building to the other, and smaller diameter pipes branch off to supply rooms or individual fixtures. If any of the branches demands water (you flush the toilet), there is less water available to all the other branches.
Since the toilet only uses cold water, there is less cold water available to your shower when the toilet is filling. This causes the water in the shower to be warmer, because there is less cold water mixing with the hot water.
There are a few ways to reduce, or eliminate this burning feeling. Probably the cheapest, is to reduce the amount of water going to the toilet.
You can reduce how quickly the toilet uses water, by simply closing the supply valve slightly. This means the toilet will take longer to fill, but will reduce the temperature fluctuation in the shower. Adjusting the supply valve can also have negative side affects, such as increased fill times, and noise.
You can also reduce the overall amount of water the toilet needs. You can accomplish this by either buying a low flow toilet, or placing a brick, jug of water, or other object in the tank. However, this method will reduce the amount of water available for each flush, so you may encounter difficulty clearing solids from the bowl.
Installing a new mixing valve in the shower, can reduce or eliminate the temperature fluctuations. Thermostatic mixing valves automatically balance the amount of hot and cold water being mixed, which will prevent drastic fluctuations in shower temperature. If the cold water flow is reduced (due to a toilet flush), the valve automatically adjusts the amount of hot water being mixed. This keeps the shower temperature more consistent, even when other fixtures are using water.
Increasing the amount of water available in the system can alleviate the problem, but will likely require a major change to the plumbing.
If you have a trunk and branch system, increasing the trunk pipe diameter and/or the branch pipe diameter (if the branch feeds the entire room) will increase the amount of water available to the fixtures.
A more drastic solution, would be to install a manifold with home runs. This would likely require a major plumbing renovation, with almost all of the plumbing changed.
In this type of system, there is a central load balancing manifold. Then for each fixture in the house, a dedicated pipe is run between the fixture and the manifold.
In the end, it's all about supply and demand. If the demand is greater than the supply, you end up with a burnt butt. The only way to avoid uncomfortable showers is to reduce demand or increase supply.
The shower temperature changes when you flush (or use water) because the pressure in that supply line has changed. This means less supply to the mixing valve in the same setting.
Modern Thermostatic mixing valves are designed to keep the total pressure constant. This means that a reduction in cold water pressure (from a flush) is detected and the mixing valve responds by reducing corresponding flow in the hot water.
EDIT: An older shower valve mixes hot and cold water very simply by proportion. Imagine you had two separate valves (one for hot and another for cold) and you turn them each to the right amount so that the temperature of the mixed water is to your liking.
Now try to think about this in terms of flow rate. If you increase the flow rate of the hot water while leaving the cold water the same -- you get a warmer mixed flow. Likewise, increasing the cold flow while leaving the hot the same -- you get a colder mixed flow.
Conceptually this is equivalent for when you reduce a water's flow.
A thermostatic valve doesn't permit flow in this simple way. Instead, it tracks the proportion of flow. So imagine you set your flow to 50% hot and 50% cold.
If the pressure of the cold water line suddenly drops (because somebody had flushed a toilet or turned on a faucet etc.) the thermostatic valve tries to maintain the same 50/50 proportion of temperatures and it will reduce the flow of hot water automatically.
So, the solution to shifting shower temperatures is to install a thermostatic mixing valve
The various answers as to why you'd get additional heat in the shower seems to be covered. But the original question also asks why you'd get cold. Again this is due to flow rate change. However, in this case what is likely happening is that there is a decrease in the overall water supply which includes the main feed into the water heater. The main water service feeding (unaltered) the shower cold line is also pushing the hot water from way back in the tank. Considering a very hot water temperature setting in the tank: the ratio of hot to cold water in the shower probably favors the cold water side. When you flush, the flow drop on the hot water side of the shower is proportionally greater (i.e. a larger amount of hot water than cold water is decreased) causing a greater drop in heat than in cold, thus the "cold shower" effect of a toilet flush. That's my theory at least.
It is a trunk and branch system like mentioned but not in the order as previously answered. I have the same problem so I'll describe my plumbing situation as yours is likely similar. The water in from the meter comes into the house (the trunk) and feeds (branches) both my toilets first (they are the closest to the entry point) then it runs the length on my bathrooms and split feeds all the cold bathroom faucets and the hot water heater. My kitchen and laundry have a separate entry from outside.
So now when I flush and that branch starts flowing, the entire flow is limited but the mixture of hot and cold at the shower faucet and since the hot water flow is 1. longer distance and 2. more biased the mixture is colder. The hot water is more biased in most cases because the typically mixtures of hot and cold water is ~40%/60% respective so cutting the percent flow on both equally will result in colder water.
When you flush the toilet tank starts refilling by opening a valve. Some water rushes through the opened valve and is diverted from the shower. Depending on how the piping is done and how wide the valve opens more or less water is diverted form the shower and the effect is more or less noticeable.
There're two ways to improve the situation. Way one (expensive) is to have enough water at all times - you do that by using huge enough diameter pipes and pipe joins everywhere. Way two (super cheapo) is to reduce diversion by limiting the flow to the tank which is easily achieved by partially closing the faucet on the pipe before the tank. You can follow both ways at the same time. Clearly the second way is much easier - you don't need to alter the piping - but its downside is that the flow to the tank will be reduced and so the tank will take more time to refill which is unlikely to cause any serious problems.
