Pressure grows with depth, so a plate standing in water is pushed harder at the bottom than at the top. Slice it into horizontal strips: each feels the weight density times its depth times its area, and adding the strips is an integral in the depth.
Select your difficulty
Pick more than one for a sheet that mixes them.
The preview can look cramped on a phone. The PDF and printed sheet come out normal.
Use 62.4 lb/ft³ for water in feet and 9800 N/m³ in meters. Give exact answers.
A vertical plate is a rectangle 2 m wide and 5 m tall. It is submerged in water with its top edge 6 m below the surface. Find the force of the water on one side.
A vertical plate is an isosceles triangle with base 4 ft and height 3 ft. It is submerged in water with its vertex at the surface and its base at the bottom, level. Find the force of the water on one side.
The end of a horizontal cylindrical tank is a circle of radius 7 ft. The tank is full of water. Find the force of the water on the end.
A vertical plate is a rectangle 3 ft wide and 2 ft tall. It is submerged in water with its top edge 3 ft below the surface. Find the force of the water on one side.
A vertical plate is an isosceles triangle with base 3 ft and height 7 ft. It is submerged in water vertex down, with its base level and 1 ft below the surface. Find the force of the water on one side.
The end of a horizontal cylindrical tank is a circle of radius 8 ft. The tank is half full of water. Find the force of the water on the end.
A vertical plate is a rectangle 2 ft wide and 8 ft tall. It is submerged in water with its top edge 2 ft below the surface. Find the force of the water on one side.
A vertical plate is an isosceles triangle with base 8 ft and height 7 ft. It is submerged in water vertex down, with its base level and 4 ft below the surface. Find the force of the water on one side.
The end of a horizontal cylindrical tank is a circle of radius 7 ft. The tank is half full of water. Find the force of the water on the end.
A vertical plate is a rectangle 6 ft wide and 8 ft tall. It is submerged in water with its top edge 4 ft below the surface. Find the force of the water on one side.
A vertical plate is an isosceles triangle with base 4 ft and height 7 ft. It is submerged in water with its vertex at the surface and its base at the bottom, level. Find the force of the water on one side.
The end of a horizontal cylindrical tank is a circle of radius 2 ft. The tank is full of water. Find the force of the water on the end.
A vertical plate is a rectangle 7 ft wide and 6 ft tall. It is submerged in water with its top edge 6 ft below the surface. Find the force of the water on one side.
A vertical plate is an isosceles triangle with base 9 ft and height 7 ft. It is submerged in water vertex down, with its base level and 4 ft below the surface. Find the force of the water on one side.
The end of a horizontal cylindrical tank is a circle of radius 3 m. The tank is half full of water. Find the force of the water on the end.
A vertical plate is a rectangle 7 ft wide and 8 ft tall. It is submerged in water with its top edge 4 ft below the surface. Find the force of the water on one side.
A vertical plate is an isosceles triangle with base 3 ft and height 2 ft. It is submerged in water with its vertex at the surface and its base at the bottom, level. Find the force of the water on one side.
The end of a horizontal cylindrical tank is a circle of radius 3 ft. The tank is half full of water. Find the force of the water on the end.
A vertical plate is a rectangle 2 ft wide and 7 ft tall. It is submerged in water with its top edge 6 ft below the surface. Find the force of the water on one side.
A vertical plate is an isosceles triangle with base 8 ft and height 9 ft. It is submerged in water vertex down, with its base level and 3 ft below the surface. Find the force of the water on one side.
Use 62.4 lb/ft³ for water in feet and 9800 N/m³ in meters. Give exact answers.
A vertical plate is a rectangle 2 m wide and 5 m tall. It is submerged in water with its top edge 6 m below the surface. Find the force of the water on one side.833000 N
A vertical plate is an isosceles triangle with base 4 ft and height 3 ft. It is submerged in water with its vertex at the surface and its base at the bottom, level. Find the force of the water on one side.748.8 lb
The end of a horizontal cylindrical tank is a circle of radius 7 ft. The tank is full of water. Find the force of the water on the end.21403.2π lb
A vertical plate is a rectangle 3 ft wide and 2 ft tall. It is submerged in water with its top edge 3 ft below the surface. Find the force of the water on one side.1497.6 lb
A vertical plate is an isosceles triangle with base 3 ft and height 7 ft. It is submerged in water vertex down, with its base level and 1 ft below the surface. Find the force of the water on one side.2184 lb
The end of a horizontal cylindrical tank is a circle of radius 8 ft. The tank is half full of water. Find the force of the water on the end.21299.2 lb
A vertical plate is a rectangle 2 ft wide and 8 ft tall. It is submerged in water with its top edge 2 ft below the surface. Find the force of the water on one side.5990.4 lb
A vertical plate is an isosceles triangle with base 8 ft and height 7 ft. It is submerged in water vertex down, with its base level and 4 ft below the surface. Find the force of the water on one side.11065.6 lb
The end of a horizontal cylindrical tank is a circle of radius 7 ft. The tank is half full of water. Find the force of the water on the end.14268.8 lb
A vertical plate is a rectangle 6 ft wide and 8 ft tall. It is submerged in water with its top edge 4 ft below the surface. Find the force of the water on one side.23961.6 lb
A vertical plate is an isosceles triangle with base 4 ft and height 7 ft. It is submerged in water with its vertex at the surface and its base at the bottom, level. Find the force of the water on one side.4076.8 lb
The end of a horizontal cylindrical tank is a circle of radius 2 ft. The tank is full of water. Find the force of the water on the end.499.2π lb
A vertical plate is a rectangle 7 ft wide and 6 ft tall. It is submerged in water with its top edge 6 ft below the surface. Find the force of the water on one side.23587.2 lb
A vertical plate is an isosceles triangle with base 9 ft and height 7 ft. It is submerged in water vertex down, with its base level and 4 ft below the surface. Find the force of the water on one side.12448.8 lb
The end of a horizontal cylindrical tank is a circle of radius 3 m. The tank is half full of water. Find the force of the water on the end.176400 N
A vertical plate is a rectangle 7 ft wide and 8 ft tall. It is submerged in water with its top edge 4 ft below the surface. Find the force of the water on one side.27955.2 lb
A vertical plate is an isosceles triangle with base 3 ft and height 2 ft. It is submerged in water with its vertex at the surface and its base at the bottom, level. Find the force of the water on one side.249.6 lb
The end of a horizontal cylindrical tank is a circle of radius 3 ft. The tank is half full of water. Find the force of the water on the end.1123.2 lb
A vertical plate is a rectangle 2 ft wide and 7 ft tall. It is submerged in water with its top edge 6 ft below the surface. Find the force of the water on one side.8299.2 lb
A vertical plate is an isosceles triangle with base 8 ft and height 9 ft. It is submerged in water vertex down, with its base level and 3 ft below the surface. Find the force of the water on one side.13478.4 lb
A vertical plate is a rectangle 4 ft wide and 3 ft tall, with its top edge 2 ft below the surface. Find the force.
Measure y as depth. The plate runs from y = 2 to y = 5, and every strip is 4 ft wide.
F = ∫ from 2 to 5 of 62.4 · y · 4 dy = 249.6 · [y²/2] from 2 to 5.
249.6 · (25 - 4)/2 = 249.6 · 10.5 = 2620.8.
The answer is 2620.8 lb.
Where students go wrong
Measuring y up from the bottom of the plate and then using y as the depth. The pressure depends on depth below the surface, so set up y that way (or write the depth in terms of your y) before integrating.
Also called fluid force, fluid pressure and force, hydrostatic pressure or force of water on a dam.
What you can put on this worksheet
Rectangular plates and gates
A vertical plate is a rectangle 6 ft wide and 5 ft tall. It is submerged in water with its top edge at the surface. Find the force of the water on one side.→ 4680 lb
Triangles and trapezoids
A vertical plate is an isosceles triangle with base 6 ft and height 6 ft. It is submerged in water vertex down, with its base along the surface. Find the force of the water on one side.→ 2246.4 lb
Circles and semicircles
A circular window of radius 3 m is set vertically in the side of a tank. Its center is 8 m below the surface. Find the force of the water on the window.→ 705600π N
Questions about these worksheets
Yes. Every hydrostatic force sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.
Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.
Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.
Calculus is usually taken around 12th grade or a first college course, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.
Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.
That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the hydrostatic force questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.
Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.
You pick from 3: rectangular plates and gates, triangles and trapezoids and circles and semicircles. Tick as many as you want and set how many of each, or let it spread them evenly.
Measuring y up from the bottom of the plate and then using y as the depth. The pressure depends on depth below the surface, so set up y that way (or write the depth in terms of your y) before integrating.