When a driver presses the brake pedal in a car, they apply a relatively small force over a small area (the master cylinder). According to Pascal's Principle, this creates a pressure increase that is transmitted undiminished through the brake fluid to the brake calipers at each wheel. Because the calipers have a much larger surface area than the master cylinder, the resulting force exerted on the brake pads is massive—enough to stop a speeding vehicle. This hydraulic multiplication of force is essential for modern transportation safety.

The cross-section of an airplane wing is shaped like an airfoil—curved on top and relatively flat on the bottom. As the plane moves forward, the air is split by the wing. To rejoin at the trailing edge at the same time, the air traveling over the curved top surface must move faster than the air moving under the flat bottom surface. According to Bernoulli's equation, this increase in fluid velocity on top results in a decrease in pressure. The higher pressure pushing up from the bottom creates a net upward force called lift.

Calculate the absolute pressure at the bottom of a $3.0 \text{ m}$ deep swimming pool filled with fresh water ($\rho = 1000 \text{ kg/m}^3$). Assume atmospheric pressure is $P_0 = 1.01 \times 10^5 \text{ Pa}$. ($g = 9.81 \text{ m/s}^2$)

A hydraulic lift in a garage has a small piston with a radius of $2.0 \text{ cm}$ and a large piston with a radius of $15.0 \text{ cm}$. What force must be applied to the small piston to lift a $1500 \text{ kg}$ car resting on the large piston?

A U-tube contains mercury ($\rho_m = 13,600 \text{ kg/m}^3$). Water ($\rho_w = 1000 \text{ kg/m}^3$) is poured into the right arm until the water column is $15 \text{ cm}$ tall. How much higher does the mercury rise in the left arm compared to the mercury-water interface in the right arm?

A solid aluminum block ($\rho_{Al} = 2700 \text{ kg/m}^3$) with a volume of $0.05 \text{ m}^3$ is completely submerged in water ($\rho_w = 1000 \text{ kg/m}^3$). Calculate the buoyant force acting on it.

The density of ice is $917 \text{ kg/m}^3$, and the density of seawater is $1025 \text{ kg/m}^3$. What percentage of an iceberg's volume is submerged below the surface of the ocean?

A spherical balloon with a radius of $0.2 \text{ m}$ is filled with helium ($\rho_{He} = 0.179 \text{ kg/m}^3$). It is tethered to the ground by a light string. What is the tension in the string? (Density of air $\rho_{air} = 1.29 \text{ kg/m}^3$).

Water flows through a horizontal pipe. At section 1, the radius is $4.0 \text{ cm}$ and the water speed is $2.0 \text{ m/s}$. The pipe narrows to a radius of $2.0 \text{ cm}$ at section 2. What is the water speed at section 2?

Using the pipe from the previous example, if the absolute pressure at section 1 ($r=4.0 \text{ cm}$, $v=2.0 \text{ m/s}$) is $1.5 \times 10^5 \text{ Pa}$, what is the pressure at section 2 ($v=8.0 \text{ m/s}$)? ($\rho_{water} = 1000 \text{ kg/m}^3$)

A large open water tank has a small hole punched in its side, $5.0 \text{ m}$ below the water surface. What is the speed of the water jet emerging from the hole?