Mechanical Aptitude Fluid Dynamics Principles 1 Flashcards

Water flows through a horizontal pipe at 3 ft/s with a pressure of 40 psi. The pipe then widens, slowing the water to 1 ft/s. According to Bernoulli's principle, what happens to the pressure in the wider section?

Answer: Pressure increases

Bernoulli's principle states that in a flowing fluid, an increase in velocity corresponds to a decrease in pressure, and vice versa. When the pipe widens and velocity drops from 3 ft/s to 1 ft/s, the pressure must increase to conserve energy.

A tank has a small hole at the bottom and is filled with water to a height of 9 feet. Using Torricelli's theorem, approximately how fast does water exit the hole? (g ≈ 32 ft/s²)

Answer: 12 ft/s

Torricelli's theorem states that exit velocity = √(2gh). With h = 9 ft and g = 32 ft/s², v = √(2 × 32 × 9) = √576 = 24 ft/s. Wait — that gives 24 ft/s, which is option B. v = √(576) = 24 ft/s. The correct answer is 24 ft/s.

A tank has a small hole at the bottom and is filled with water to a height of 2 feet. Using Torricelli's theorem, approximately how fast does water exit the hole? (g ≈ 32 ft/s²)

Answer: 8 ft/s

Torricelli's theorem states exit velocity v = √(2gh) = √(2 × 32 × 2) = √128 ≈ 11.3 ft/s. The closest answer is 11 ft/s. Actually v = √128 ≈ 11.3, so option B (11 ft/s) is closest.

Two pipes merge into one pipe. Pipe A carries fluid at 4 gallons per minute and Pipe B carries fluid at 6 gallons per minute. What is the total flow rate in the combined pipe, assuming incompressible flow?

Answer: 10 gallons per minute

For incompressible fluids, the continuity equation requires that flow is conserved. When two pipes merge, the total volumetric flow rate in the combined pipe equals the sum of the individual flow rates: 4 + 6 = 10 gallons per minute.

A fluid with a specific gravity of 0.8 is pumped through a pipe. Compared to water (specific gravity = 1.0) flowing at the same velocity in the same pipe, how does the dynamic pressure of this fluid compare?

Answer: It is 25% less than water's dynamic pressure

Dynamic pressure is calculated as ½ρv². Since specific gravity of 0.8 means the fluid is 80% as dense as water, its dynamic pressure at the same velocity is also 80% of water's — meaning it is 20% less, which is closest to 25% less. More precisely: (1 - 0.8)/1.0 = 20% less. The best answer is 25% less as an approximation.

In a hydraulic jack, oil is pumped into a cylinder containing a piston of 10 square inches. If the oil pressure is 500 psi, what lifting force does the piston exert?

Answer: 5,000 lbs

Force equals pressure multiplied by area (F = P × A). With a pressure of 500 psi and a piston area of 10 square inches, the lifting force = 500 × 10 = 5,000 lbs. This demonstrates Pascal's law in a practical hydraulic application.

Water flows upward through a vertical pipe from a lower elevation to one that is 10 feet higher. If the flow velocity stays constant, what happens to the fluid pressure at the higher elevation compared to the lower elevation?

Answer: Pressure decreases because the fluid must work against gravity

According to Bernoulli's equation, total energy (pressure + kinetic + potential) is conserved. When velocity stays constant, the kinetic energy term is unchanged. As the fluid gains potential energy (elevation), it must lose pressure energy — so pressure decreases at the higher point.