Bernoulli's Basics
Per Bernoulli's principle, when the speed of a fluid increases, what happens to its pressure?
The pressure decreases.
What is the continuity equation?
A1v1 = A2v2
In Big Noulli's equation, what does 1/2 pv^2 represent?
Kinetic energy per unit volume
How does Bernoulli's principle help explain lift on an airplane wing?
Faster air over part of the wing creates lower pressure, producing a pressure difference that contributes to lift.
In funnel and ping-pong ball demo, what should happen when air moves quickly around the ball?
(provided we actually demoed this properly)
The ball should stay in or near the funnel, rather than falling.
Bernoulli's equation is based on the conservation of what?
Energy
If a pipe gets narrower, what happens to the speed of the fluid?
The fluid speeds up.
In Big Noulli's equation, what does pgh represent?
Gravitational potential energy per unit volume.
What is the Magnus effect?
The curving motion of a spinning object moving through a fluid, caused by different air speeds and pressures on opposite sides. (like the soccer ball)
Why does air speed increase near the narrow part of the funnel?
The area is smaller, so by continuity, the air must move faster.
What are the three main energy terms in Bernoulli's equation?
Pressure energy, kinetic energy, and gravitational potential energy
Water flows through a pipe of area 4m^2 at 3 m/s. What is the flow rate?
If two points in a pipe are at the same height, which term cancels out in Bernoulli's equation?
pgh
Why is the path of a spinning soccer ball curved?
Why does the fast-moving air around the ping-pong ball create low pressure?
Faster air has more kinetic energy, so the pressure energy is lower.
Write the general form of Bernoulli's equation.
P1 + 1/2pv1^2 + pgh1 = P2 + 1/2pv2^2 + pgh2
this stupid website tried to make me pay $20 to write that in asciimath
A pipe narrows from A1 = 6m^2 to A2 = 2m^2. If v1 = 3m/s, find v2.
9 m/s
Water in a level pipe speeds up from 2 m/s to 5 m/s. What happens to pressure?
Pressure decreases (because kinetic energy increases)
If you blow over the top of a strip of paper, increasing the velocity of the air above it, what will happen to the paper?
The paper will rise (lower pressure above, higher pressure below)
Which two equations/principles work together in the funnel demo?
Continuity equation and Bernouli's principle.
Explain why faster-moving fluid usually has lower pressure.
With an increase in kinetic energy comes a decrease in another form of energy. In a level flow, that usually comes from pressure energy, so pressure drops.
Why does the continuity equation work for a non-compressible fluid?
The fluid can't build up or disappear inside of the pipe, so the same amount of fluid must pass through each section every second.
Water flows through a level pipe. At point 1, P1 = 120,000 Pa and v1 = 2 m/s. At point 2, v2 = 6 m/s. p = 1000 kg/m^3. Find P2.
Two sheets of paper are hanging next to each other. You blow air between them. What happens?
The sheets of paper pull toward each other (the pressure between them decreases)
The narrow part of the funnel makes air move faster because of continuity. The faster-moving air creates lower pressure around the ball because of Bernoulli's principle. (higher surrounding pressure keeps the ball in place)