Optional Unit VI: Fluid Mechanics
C. Pascal's Principle

Key Concepts

Pressure exerted on an enclosed liquid is transmitted equally to every part of the liquid and to the walls of the container. (Pascal's principle)

A manometer relies on Pascal's principle to measure pressure in gases.

Pascal's principle is important in understanding hydraulics, the study of the transfer of forces through fluids.

In a hydraulic lift, a force (F) applied to an input piston having a small surface area (A_(in)) is transferred to an output piston having a larger surface area (A_(out)). There is no loss in pressure from the input to the output pistons (neglecting friction). As a result, the output force (F_(out))is much larger than the input force (A_(out)).

P_(out) = P_(in) (Pascal's principle)

F(out)	=	F(in)
A(out)		A(in)

Due to conservation of energy, and , the small piston has to travel a proportionately greater distance, d.

F_in · d_in = F_out · d_out

Alternatively, since the volume moved is constant,

d_in · A_in = d_out · A_out

The mechanical advantage of a hydraulic lift is given by:

Mechanical advantage =	F(out)	=	F(in)
	A(out)		A(in)

Learning Outcomes

1. Define the following terms: manometer, hydraulics, hydraulic lift.

2. State Pascal's principle.

3. Give some examples which illustrate Pascal's principle.

4. Explain why the output force on a hydraulic lift exceeds the input force.

5. Solve problems involving Pascal's principle.

Teaching Suggestions, Activities and Demonstrations

1. Experimentally investigate pressure in liquids. Challenge students by posing the problem to be considered experimentally. See if they can come up with their own experimental designs.

2. Bring in a used carburettor from an automobile. (Some students may have access to these.) Examine the venturi. Explore the principles which make the carburettor operate.

3. Take a short length of used vacuum cleaner hose and spin it in a circle to produce an interesting sound. The class can speculate as to how the sound is produced.

4. Cut out wooden blocks having different shapes. Predict their orientation when they float in water. Irregular shaped blocks may float in some interesting ways. Relationships between the orientation for stable equilibrium, the shape of the block, and the centre of gravity can be made. This activity provides students with an understanding of how predictions are made in science.