Question

A barrel 1 m tall and 60 cm in diameter is filled to the top with water. What is the pressure it exerts on the floor beneath it? What could you do to reduce this pressure without removing the water?

Answer 1

The pressure on the ground is about 9779.5 Pascal.

The pressure can be reduced by distributing the weight over a larger area using, for example, a thin plate with an area larger than the circular area of the barrel's bottom side. See more details further below.

Step-by-step explanation:

Start with the formula for pressure

(pressure P) = (Force F) / (Area A)

In order to determine the pressure the barrel exerts on the floor area, we need the calculate the its weight first

`F_g = m \cdot g`

where m is the mass of the barrel and g the gravitational acceleration. We can estimate this mass using the volume of a cylinder with radius 30 cm and height 1m, the density of the water, and the assumption that the container mass is negligible:

`V = h\pi r^2=1m \cdot \pi\cdot 0.3^2 m^2\approx 0.283m^3`

The density of water is 997 kg/m^3, so the mass of the barrel is:

`m = V\cdot \rho = 0.283 m^3 \cdot 997 (kg)/(m^3)= 282.151kg`

and so the weight is

`F_g = 282.151kg\cdot 9.8(m)/(s^2)=2765.08N`

and so the pressure is

`P = (F)/(A) = (F)/(\pi r^2)= (2765.08N)/(\pi \cdot 0.3^2 m^2)\approx 9779.5 Pa`

This answers the first part of the question.

The second part of the question asks for ways to reduce the above pressure without changing the amount of water. Since the pressure is directly proportional to the weight (determined by the water) and indirectly proportional to the area, changing the area offers itself here. Specifically, we could insert a thin plate (of negligible additional weight) to spread the weight of the barrel over a larger area. Alternatively, the barrel could be reshaped (if this is allowed) into one with a larger diameter (and smaller height), which would achieve a reduction of the pressure.