in this lesson we're going to talk about pressure pressure is force divided by area in physics the standard unit of pressure is pascals one pascal is one newton per square meter and one kilopascal is a thousand pascals and one atm or atmospheric pressure is 101.3 kilopascals so those are some units that you want to keep in mind so whenever you exert a force over a given area that force exerts a pressure throughout that area so pressure is simply force over area now what happens if you increase the area but use the same force let's say if we double the dimensions now if you apply us the same force over let's say a larger area the pressure is going to be a lot less let's say if we apply a force of a hundred newtons the pressure in this example is a hundred divided by one square meter so it's a hundred pascals in the second example the area is two times two which is uh four so the pressure is now a force of 100 newtons divided by an area of four square meters so it's 25 pascals so what you need to understand is that if you increase the force applied the pressure increases if you increase the area in which that force is applied the pressure decreases the pressure is directly related to the force but inversely related to the area upon which that force is applied let's try this problem a 15 kilogram rectangular block with a length of 70 centimeters and the width of 40 centimeters rests on the table what pressure does the book exert on the table so let's say this is the book and it's on a table now that book is going to exert a weight force on the table and that force is applied over the area of the book the bottom area now we have a length that's 70 centimeters and a width of 40 centimeters and we know that pressure is force divided by area and the force that the book exerts is basically the weight force of the book which is mg so the pressure exerted by the book is just mg divided by the area of the book so the mass of the book is 15 kilograms the gravitational acceleration is 9.8 and the area let's get it in square meters so to convert centimeters to meters divide by a hundred seventy centimeters is point seven meters and forty centimeters is point four meters so 15 times 9.8 so that's going to give us a force of 147 units and 0.7 times 0.4 that's going to give us an area of 0.28 square meters so if we divide these two numbers the pressure exerted by this book alone is 525 pascals so this is the answer number two a closed rectangular container with dimensions four meters by five meters by six meters is filled with water what is the pressure exerted by the water on the bottom face of the container so let's draw a rectangular container and it's filled with water now our goal is to find the pressure that's exerted by the weight of the water on the bottom surface of the cube so how can we do that well we know pressure is force over area and keep in mind the density of water if you're wondering is a thousand kilograms per cubic meter now the force is the weight of the water which is mg and we don't have the mass of the water however we know that density which is rho is mass over volume don't confuse this with pressure so the mass of the fluid if we multiply both sides by v is density times the volume so the pressure of the fluid is going to be the mass which is density times volume and then times gravitational acceleration divided by the area now the volume of let's say this rectangular prism is the length times the width times the height so let me write that somewhere now the length times the width will give us the area of the bottom surface or rather i'm just going to replace volume with length times width times height and the area of the bottom surface is just the length times the width so we could cancel l and w so the pressure that's due to the weight of the water alone is going to be the density of the fluid times the gravitational acceleration times the height of the fluid so here it is this is the equation that you want to keep in mind when dealing with the pressure due to a fluid so we know the density of water is a thousand kilograms per cubic meter we have the gravitational acceleration it's 9.8 and the height of the fluid now let's say the first one is the length the second is the width so the height we're going to say it's 6 meters in this example so it's going to be a thousand times 9.8 times 6. the pressure is 58 800 pascals so that's the pressure due to the weight of the water alone number three a closed cylindrical container is filled with a fluid that has a specific gravity of 1.7 what is the pressure exerted by this fluid at a depth of 50 meters so let's say this is the cylindrical container and it's closed and it's filled with some fluid so at a depth of 15 feet i mean that fifa 15 meters let's say at this point we want to know what's the pressure exerted at that depth so we can use this equation the pressure is equal to the density times gravity times the height so if you have a fluid and you want to find the pressure exerted by the fluid alone at a certain depth this is the equation that you can use now we need to know what the density of this fluid is and we're given that specific gravity the specific gravity is the density of the substance in this case the density of fluid relative to the density of water so the density of the fluid is going to be the specific gravity times the density of water so we have a specific gravity 1.7 and the density of water is a thousand kilograms per cubic meter so the density of the fluid is 1700 kilograms per cubic meter now we have the gravitational acceleration and the depth is 15 meters so it's 1700 times 9.8 times 15. so the pressure exerted by this fluid at a point where it's 50 meters deep is 249 900 pascals and if you divide that by a thousand you could say it's about 249.9 kilo pascals you