A hydraulic jack has a small piston of area 10 cm² and a large piston of area 1,000 cm². A force of 50 N is applied to the small piston. What force does the large piston exert?
A50 N — force is conserved in a closed hydraulic system
B0.5 N — the pressure is distributed over a larger area, reducing force
C5,000 N — pressure is transmitted equally throughout the fluid (Pascal's principle)
D5,000 N only if both pistons are at the same height
Pascal's principle: pressure applied at one point in a static connected fluid is transmitted equally to all other points. Pressure at small piston = 50 N / 0.001 m² = 50,000 Pa. The large piston (0.1 m²) experiences the same pressure: F = 50,000 × 0.1 = 5,000 N. This 100× mechanical advantage is how hydraulic jacks, brakes, and presses work. Option A confuses force with pressure; pressure (not force) is what transmits equally.
Question 2 Multiple Choice
A flat rectangular gate is mounted vertically in a dam, with its top edge at the water surface. Where does the resultant hydrostatic force on the gate act?
AAt the geometric centroid of the gate — the midpoint of the vertical dimension
BAbove the centroid — water pressure is highest at the surface where most water contacts the gate
CBelow the centroid — deeper portions experience higher pressure and contribute more force
DUniformly across the gate — pressure is isotropic so no single point of application exists
Hydrostatic pressure increases linearly with depth (P = P₀ + ρgh), so the bottom of a vertical gate is under higher pressure than the top. The resultant force is the integral of pressure over area, weighted toward the deeper, higher-pressure portions. This shifts the center of pressure below the geometric centroid. Designing gates and dam faces requires finding this center of pressure — not the centroid — to correctly place structural supports.
Question 3 True / False
In a fluid at rest, pressure acts more strongly in the downward (vertical) direction than horizontally, because gravity is what creates the pressure.
TTrue
FFalse
Answer: False
Pressure in a static fluid is isotropic — at any given point and depth, it acts equally in all directions. Gravity causes pressure to increase with depth, but at a specific depth the pressure magnitude is the same whether you measure it acting upward, downward, or sideways. This isotropy is what allows pressure to transmit through a fluid in all directions, which is the basis for Pascal's principle and hydraulic machines. It distinguishes pressure in fluids from directed forces in solids.
Question 4 True / False
Gauge pressure equals absolute pressure minus atmospheric pressure.
TTrue
FFalse
Answer: True
Absolute pressure is measured from perfect vacuum. Gauge pressure subtracts atmospheric pressure (the reference the gauge experiences on its exterior), so gauge = absolute − atmospheric. A tire at '32 psi gauge' has absolute pressure of roughly 32 + 14.7 ≈ 46.7 psi. In engineering calculations involving forces on surfaces exposed to atmosphere on one side, gauge pressures automatically cancel the atmospheric contribution, simplifying the math — which is why gauge pressure is the working standard.
Question 5 Short Answer
Why must a dam be structurally stronger (thicker or more reinforced) at its base than at its top, even though the dam surface area is the same at all depths?
Think about your answer, then reveal below.
Model answer: Because hydrostatic pressure increases linearly with depth: P = P₀ + ρgh. The water at the base of the dam exerts far greater pressure per unit area than water near the surface. Since force equals pressure times area, and the area is the same at every depth, the force on base sections is proportionally larger. The base must resist this greater force, requiring greater structural strength than the top.
This is a direct application of the hydrostatic pressure distribution. At the water surface h = 0, so pressure equals atmospheric. At depth h, pressure has increased by ρgh — for a 30m dam with water (ρ = 1000 kg/m³), that's an additional ~294,000 Pa at the base. The force on a 1 m² section at the base is roughly 294 kN more than at the surface. Ignoring this gradient would lead to catastrophic structural failure at the base, as famously illustrated in historical dam failures.