Final answer:
The pressure at the bottom of the water tank will be 2.6P after the water level is reduced by one-fifth. This takes into account the initial pressure of 3P, which decreases proportionally to the reduction in the depth of water.
Step-by-step explanation:
The pressure at the bottom of a tank of water is given by the sum of atmospheric pressure and the pressure due to the weight of the water column above the bottom point. Initially, the pressure at the bottom is 3P, where P is the atmospheric pressure. When the level of water is reduced by one-fifth, the depth of the water column decreases, therefore also decreasing the pressure due to the weight of the water column.
Since pressure due to a fluid in a container is proportional to the height of the fluid column, which in this case is the depth of water (h), given as P = ρgh, where ρ is the fluid density and g is the acceleration due to gravity, a decrease in h by one-fifth would correspond to a similar reduction in pressure.
If the original water column resulted in a pressure of 2P (since total pressure is 3P, which consists of atmospheric pressure P and pressure due to water column 2P), then reducing the height by one-fifth would reduce the pressure by one-fifth of 2P, which is 0.4P. Hence, the new pressure due to the water column will be 2P - 0.4P = 1.6P. The new total pressure at the bottom will be the sum of atmospheric pressure P and the reduced water column pressure 1.6P, which gives 2.6P.