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

When a boat enters a lock, what forces are exerted? The boat does not touch the sides of the lock directly. Instead the water level rises. The pressure at each point in the water is due to the pressure of the water above that point plus atmospheric pressure. Suppose a boat of mass 1000kg enters a lock 5m deep, 10 long and 5m wide.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 (\[W= mg=1000 \times 9.8=9800N\]

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