## Increase in Water Pressure As a Result of a Boat Entering a Lock

According to Archimedes principle 1000kg of water is displaced. Water has a density of 1000kg per cubic metre, so 1 cubic metre of water is displaced. The increse in the water level is

\[\Delta h= \frac{\Delta V}{A}=\frac{1}{10 \times 5}=0.02 m\]

or 2 cm.The increase in pressure is due solely to this extra 2cm depth of water. The increasde in pressure is

\[\Delta P= \rho g \Delta h = 1000 \times 9.8 \times 0.02 =196 Pa\]

.This is a comparatively small increase in pressure less than 0.2% of atmospheric pressure (

\[p_{Atmospheric} \simeq 10^5Pa\]

).The increase in the force on the bottom of the the lock is

\[|Delta F = A \delta P= 10 \times 5 \times196=9800N\]

and this is equal to the weight of the boat (\[W= mg=1000 \times 9.8=9800N\]

)