Whiteboard Warmup: AP FRQ from 2005

A large rectangular raft of density 650 kg/m3 is floating on a lake. The surface area of the top of the raft is 8.2 m2 and its total volume is 1.80 m3. The density of the lake water is 1,000 kg/m3.

Calculate the height h of the portion of the raft that is above the surrounding water.

Life Raft Solution

FB = ρfluidVsubmergedg

Mg = ρobjectVtotalg

65% of the raft is submerged, therefore 35% of the raft will be sticking out of the water!

To find total height, use V = Ah!

Fluid Flow Group Challenge!The large container shown in the cross-section below is filled with a liquid of density 1.1 x 103 kg/m3. A small hole of area 2.5 x 10-6 m2 is opened in the side of the container, which allows a stream of liquid to flow into a beaker placed to the right of the container. At

the same time, liquid is also added to the container at an appropriate rate so that h

remains constant. The amount of liquid collected in the beaker in 2.0 minutes

is 7.2 x 10-4 m3.

What is the speed of the liquid coming out of the hole?

Hint: You will need to determine the volume rate of flow of the liquid.

Fluid Flow Solution

Using given info, v = 2.4 m/s

If we were given d, we could determine

where to place the beaker for a direct

hit

Brief Recap of Fluid Flow

A1 A2

v1 v2

The same amount of volume must pass any part of the pipe per unit time.

This means that the fluid travels faster in the smaller portion of the pipe.

Today’s Challenge: Compare the pressure in the

slow moving fluid to the pressure in the fast moving

fluid

v1 v2

Amazing Whiteboard Concept Time!

v1 v2

By following the journey of a single water molecule as it flows through the entire section of pipe, determine which portion of the pipe has the largest pressure, and which has the lowest pressure!

Hint: Think about what must be true in order for the water to speed up in between the sections of the pipe!

In order for the water molecules to travel faster in the smaller section, they must accelerate as the pipe’s radius decreases.

What is the only thing that could cause them to accelerate?

A higher pressure behind them!

This is called a pressure differential, and will cause an unbalanced force that accelerates the water into the smaller section of pipe

Highpressure

Lowpressure

In this section of pipe, the water molecules will feel a large force from the high-pressure fluid behind them, and a small

force from the low-pressure fluid in front of them.

Force exerted by high pressure fluid

Force exerted by low pressure fluid

Net force

Bernoulli’s Principal

A fast-moving fluid will have a lower pressure than a slow-moving fluid!

v1 v2

Slow-moving, high pressure

fluid

Fast-moving, low pressure

fluid

Whiteboard PredictionA T‑shaped tube with a constriction is inserted in a vessel containing a liquid, as shown above. What happens if air is blown through the tube from the left, as shown by the arrow in the diagram? (A)The liquid level in the tube rises to a level above the surface of the liquid surrounding the tube.(B) The liquid level in the tube falls below the level of the surrounding liquid.(C) The liquid level in the tube remains where it is.(D) The air bubbles out at the bottom of the tube.(E) Any of the above depending on how hard the air flows.

Patm

Patm Patm

Fast-moving airLess than Patm

Patm Patm

Fast-flowing fluids have lower pressure!

The pressure above the straw lowers, allowing the atmosphere to actually push the water upward into the straw!

Bernoulli Ball!

Wings: Explained!

The reason why the air above the wing travels faster is a complex property of airfoil design.

Curveballs: Explained!

Since the ball is spinning forward, the air above the ball is slowed down significantly (by friction), while the air below the ball flows smoothly under it. This creates slower, higher-pressure air above!

The pressure differential causes the ball to drop faster than ay = -g