FCTC Mechanical Reasoning Principles 2 — Questions and Answers

Question 1: A fire pump uses a centrifugal impeller. What happens to water pressure output if the pump speed is doubled?

Pressure doubles
Pressure increases by a factor of 4 (Correct answer)
Pressure stays the same
Pressure is cut in half

Correct answer: Pressure increases by a factor of 4

For centrifugal pumps, pressure (head) increases with the square of the speed. Doubling speed quadruples pressure output.

Centrifugal pump laws (affinity laws) state that pressure (head) varies with the square of the impeller speed: P₂/P₁ = (N₂/N₁)². If speed doubles (N₂ = 2N₁), then P₂ = P₁ × (2)² = 4P₁. So pressure quadruples. This principle is why pump operators must carefully control engine RPM — small speed increases produce large pressure changes. Flow rate increases proportionally (not squared) with speed, while power required increases with the cube of speed.

Question 2: A hydraulic spreader (Jaws of Life) uses fluid to generate force. Which principle explains how a small force on the input cylinder creates a larger force on the output cylinder?

Boyle's Law
Pascal's Law (Correct answer)
Bernoulli's Principle
Newton's Third Law

Correct answer: Pascal's Law

Pascal's Law states that pressure applied to a confined fluid is transmitted equally in all directions. A larger output piston area multiplies the force.

Pascal's Law: Pressure is transmitted undiminished throughout a confined, incompressible fluid. In a hydraulic rescue tool: Force = Pressure × Area. A small input force on a small piston creates pressure (F/A). That same pressure acts on a much larger output piston area, generating a proportionally larger output force. For example, 100 lbs on a 1-in² piston creates 100 psi. That 100 psi on a 20-in² output piston produces 2,000 lbs — a 20:1 mechanical advantage.

Question 3: A firefighter uses a Halligan bar as a class 1 lever to force a door. If the fulcrum is 3 inches from the load end and the firefighter applies force at 24 inches from the fulcrum, what is the mechanical advantage?

4
6
8 (Correct answer)
10

Correct answer: 8

Mechanical Advantage = Effort Arm ÷ Load Arm = 24 ÷ 3 = 8.

Mechanical Advantage (MA) = Effort Arm ÷ Load Arm = 24 inches ÷ 3 inches = 8. This means the firefighter's input force is multiplied by 8 at the door jamb. If the firefighter applies 50 lbs of force, the tool delivers 400 lbs of force at the load. The Halligan bar is a first-class lever (fulcrum between effort and load) optimized for forcible entry. Understanding mechanical advantage helps firefighters select the right tool and technique for different door and lock types.

Question 4: What type of pulley system would a firefighter use to lift a victim from a below-grade confined space with the greatest mechanical advantage using a single movable pulley?

Fixed pulley — 1:1
Movable pulley — 2:1 (Correct answer)
Block and tackle — 4:1
Z-rig — 3:1

Correct answer: Movable pulley — 2:1

A single movable pulley creates a 2:1 mechanical advantage, halving the effort required to lift the load.

A fixed pulley changes direction of force but provides no mechanical advantage (1:1 ratio). A single movable pulley creates a 2:1 mechanical advantage — the load is supported by two rope segments, so each carries half the weight. To lift a 200-lb victim, only 100 lbs of effort is required (ignoring friction). In confined space rescue, pulley systems are critical when lifting injured or unconscious victims who cannot assist in their own rescue. More complex systems (Z-rig, C-rig) provide higher mechanical advantage for heavier loads.

Question 5: Which type of gear arrangement is used when two gears mesh together with teeth, and turning the first gear clockwise causes the second gear to turn counterclockwise?

Worm gear
Planetary gear
Spur gear (Correct answer)
Bevel gear

Correct answer: Spur gear

Spur gears are the simplest meshing gears — when two spur gears mesh, they rotate in opposite directions. The driving gear turns clockwise, the driven gear turns counterclockwise.

Spur gears have teeth cut parallel to the axis of rotation and mesh directly with each other. When two external spur gears engage, they rotate in opposite directions — clockwise input produces counterclockwise output. This is the most basic gear arrangement seen in mechanical systems. In fire apparatus, gears appear in transmission systems, pump drives, aerial ladder hydraulic systems, and power take-off (PTO) units. Understanding gear rotation direction is tested in mechanical reasoning assessments.

Question 6: A fire hose nozzle is attached at the end of 100 feet of hose. What happens to water velocity as the water passes through the nozzle opening (assuming nozzle diameter is smaller than hose diameter)?

Velocity decreases
Velocity stays the same
Velocity increases (Correct answer)
Velocity becomes zero

Correct answer: Velocity increases

According to the continuity equation (conservation of mass), when cross-sectional area decreases, fluid velocity must increase to maintain the same flow rate.

The continuity equation states: A₁ × V₁ = A₂ × V₂ (for incompressible flow). If the nozzle area (A₂) is smaller than the hose area (A₁), then V₂ must be greater than V₁ to maintain flow continuity. This is why water exits a nozzle at high velocity and can reach the seat of a fire. Nozzle design specifically exploits this principle — the tip diameter is engineered to produce the velocity and stream shape needed for effective firefighting at specific operating pressures.

FCTC Mechanical Reasoning Principles 2

A fire pump uses a centrifugal impeller.
What happens to water pressure output if the pump speed is doubled?