Thinking About Physics in the Shower…

I recently spent a night at a hotel with one of those fancy, multi-setting shower heads. Having just learned about fluid mechanics in physics class, I was thinking about how physics can be used to explain these different settings. Here I will analyze only two settings: spray versus massage.

In both of these cases water travels to the shower head through the same ascending tube and thus has all the same initial flow properties. How the water exits the shower head, then, it what determines what the shower will feel like. The feel of the shower is mainly dependent upon exiting water pressure. Different pressures can be achieved through having different hole sizes for the water to flow through.

It is possible to use the equation ρ₁A₁v₁= ρ₂A₂v₂ to find the relative speed of the water exiting the shower head. Smaller holes have smaller cross-sectional areas and as a result the water exiting them has a larger velocity than water exiting the larger holes. Through comparisons using Bernoulli’s equation, P₁+1/2(ρ)(v₁²)+ρgh₁= P₂+1/2(ρ)(v₂²)+ρgh₂, water with a larger final velocity must have a smaller final pressure in order to follow the law of conservation of energy. On the flip side, water exiting larger holes has a higher pressure. This is how the massage setting is achieved. The spray setting, in comparison, merely has smaller holes for the water the flow through. Shower head manufacturers thus play with these simple physics principles to create multiple shower flow settings.