# Why is there an upthrust?

Why is there $$P_2$$?
Is it because by Newton's third law of motion, $$P_2$$ is there due to the pressure of water column of $$0.7 ~m$$ above the bottom. • Can you give a more detailed explanation on the picture, maybe as a text in the textbook? – Matthew Roh Aug 3 at 4:24
• There isn't a text related to this question, but I have uploaded a new photo of the entire question. – Lim Jia Tzer Aug 3 at 4:33

For an immersed object in water, water exerts pressure on it at every point, the magnitude given by $$P=P_{atm}+\rho gh$$ h is the height of water column above that point. For the top surface, water exerts pressure downwards. For the bottom surface, water exerts pressure upwards. The water also exerts pressure on lateral sides, but is equal from all sides, since it is at same height. Hence no net effect. The pressure is higher at greater depths, so the box would experience a net upward force from below.

• Adding to the question, why is the calculation of P2 using rho(gh) – Lim Jia Tzer Aug 3 at 10:31
• The liquid pressure at a depth doesn't change even if something is submerged in it. A simple explanation is that the water still surrounds the box, the water below is not isolated from the rest of water. As a result, pressure at all points at same height is same.. – HS Singh Aug 3 at 14:28

Imagine a pool and a volume of water, say a cube of 1 litre, inside it. This volume of water is in equilibrium with the rest of the water. If not it would sink, float or move in any direction. Therefore the remaining water must exert an upward force equal to the weight of this 1 litre volume. It is clear that thus argument holds for any size or shape and for any material filling that shape. This is how Archimedes reasoned in the 3d century BC.

Water pressure is everywhere in the water, it's only unnoticeable due to not-so-deep depths. In general, water pressure increases $$1 atm$$ every $$10m$$, with the pressure on the surface being $$1 atm$$. So, calculate the pressure with this relation, and calculate the force by-

$$P=\frac{F}{A}$$

also, notice that you have to convert the pressure to Pascals here, remember that $$1 atm$$ equals $$101325 Pa$$.

• But why is there pressure acting upwards on the block by water – Lim Jia Tzer Aug 3 at 4:45
• @LimJiaTzer Simply said, Water pressure pushes the object from every direction. – Matthew Roh Aug 3 at 4:46
• It is not unnoticeable at any depth. – my2cts Aug 3 at 9:21
• @my2cts I meant the net force is unnoticeable – Matthew Roh Aug 3 at 10:13

There is pressure on the bottom because it is not in a vacuum. Water pressure increases with depth, so there is greater pressure at the bottom than at the top. That is why Pressure 2 is greater than Pressure 1. If the object weighed less than the amount of water it displaced then Pressure 2 would be greater than it's weight plus Pressure 1, and it would float upwards. If it weighed more than the amount of water it displaced then Pressure 2 would be less than it's weight plus Pressure 1 and it would sink downwards.