Video Transcript
The pressure from water at a depth 𝑑 is 21560 pascals. Find the depth 𝑑 using a value of 1000 kilograms per metre cubed for the density of water.
Okay, so in this question, we’ve got some water. And we’re looking at the pressure exerted by that water at a certain depth, which we’ve called 𝑑. In other words, if we were to place a random object at this depth below the surface of the water, depth 𝑑, we’ve been told the pressure exerted by the water on the object at this depth. And we need to figure out what the depth actually is.
To do this, we can recall the equation that gives us the pressure exerted by a liquid at a certain depth. The equation in question tells us that the pressure exerted by the liquid at a certain depth is equal to the density of the liquid multiplied by the gravitational field strength of the Earth multiplied by the depth in question.
Now in this case, we’re trying to find out the value of 𝑑. So we need to rearrange the equation by dividing both sides by 𝜌𝑔. Doing this leaves us with 𝑃 divided by 𝜌𝑔 on the left-hand side and 𝑑 on the right-hand side, at which when we can substitute in values.
We’ve been told that the pressure firstly is 21560 pascals. So we substitute that in. And then we’ve been told that the density of water is 1000 kilograms per metre cubed. And the liquid we’re studying in this question is actually water. So we substitute that in as well.
And finally, we need to sub in the value of the gravitational field strength on Earth. Now we haven’t actually been given this information in the question. But luckily, we can recall that the gravitational field strength of Earth is a constant at 9.8 meters per second squared. So we sub that value in as well.
Now at this point, we can evaluate the left-hand side of the equation to give us a value of 𝑑. When we do this, we find the value of 𝑑 to be 2.2 metres. Hence, this is our final answer.
