Unit 14: Fluid Mechanics
Pressure, buoyancy, and the continuity and Bernoulli equations that explain why a wing lifts and a hose sprays farther.
6 topics · 20 questions
Each topic is a path, not a menu: work down it in order and every question builds on the one above. Click any of them to watch the answer draw itself.
Density and Pressure
- How it worksHow does spreading the same force over a larger area reduce the pressure it produces?
- Worked exampleFind the pressure exerted by a 70 kg person standing on a shoe sole of area 0.02 m2.
- Common mistakeWhy isn't pressure the same thing as force, even though pressure comes directly from a force?
Your turn1 of 2
A person of mass m stands on a shoe sole of area A, with gravitational acceleration g. Write an expression, in terms of m, A, and g, for the pressure they exert on the ground.Pressure in a Fluid at Rest
- How it worksHow does the weight of fluid stacked above a point add up to determine the pressure there?
- Worked exampleFind the pressure 10 m below the surface of water, taking atmospheric pressure as 1.01e5 Pa and water density as 1000 kg/m3.
- Common mistakeWhy doesn't the shape of a container change the pressure at a given depth inside a fluid?
Your turn1 of 2
Water has atmospheric pressure P0 at its surface and density rho. Write an expression, in terms of P0, rho, and h, for the pressure at depth h below the surface (g = 9.8).Pascal's Principle and Hydraulic Systems
- How it worksHow does a pressure change applied anywhere in an enclosed fluid transmit unchanged to every other point?
- Worked exampleFind the output force of a hydraulic lift with input area 0.01 m2 and output area 0.5 m2 for a 200 N input force.
- Common mistakeWhy doesn't a hydraulic lift multiplying force give you extra energy for free?
Your turn1 of 2
A hydraulic lift has an input piston of area Ain and an output piston of area Aout. Write an expression, in terms of Fin, Aout, and Ain, for the output force produced by an input force Fin.Buoyancy and Archimedes's Principle
- How it worksHow does the weight of the fluid an object displaces determine exactly how much buoyant force pushes back up on it?
- Worked exampleFind the buoyant force on a 0.02 m3 block fully submerged in water of density 1000 kg/m3.
- Common mistakeWhy doesn't an object's own weight alone determine whether it floats, independent of its shape?
- Going furtherWhat happens to the buoyant force on a floating object if you hollow out its center without changing its outer shape?
Your turn1 of 2
A 0.0363 cubic meter block is fully submerged in water of density 1000 kg/m3. What buoyant force acts on it, in newtons (g = 9.8 m/s2)?Fluid Dynamics and the Continuity Equation
- How it worksHow does the continuity equation guarantee that a fluid speeds up wherever a pipe narrows?
- Worked exampleFind the speed of water in a pipe of area 0.002 m2 if it flows at 4 m/s through a wider section of area 0.008 m2.
- Common mistakeWhy doesn't the same volume of fluid flowing through a narrow pipe move at the same speed as it does in a wide one?
Your turn1 of 2
Water flows at 6 m/s through a pipe section of area 79 square centimeters. What is its speed in a narrower section of area 29 square centimeters?Bernoulli's Equation
- How it worksHow does Bernoulli's equation trade pressure for speed along a streamline while keeping total energy fixed?
- Worked exampleFind the pressure difference across a wing where air moves at 60 m/s on top and 50 m/s on the bottom, air density 1.2 kg/m3.
- Common mistakeWhy isn't Bernoulli's principle simply saying that faster-moving fluid pushes harder on its surroundings?
- Ties togetherHow does Bernoulli's equation reduce to ordinary conservation of energy when a fluid isn't moving at all?
Your turn1 of 2
Air moves at 72 m/s over the top of a wing and 43 m/s under the bottom, with air density 1.2 kg/m3. Using Bernoulli's equation (ignoring height differences), what is the pressure difference between the bottom and the top, in pascals?