Mechanical Aptitude Fluid Dynamics Principles Flashcards

An incompressible fluid flows through a horizontal pipe that narrows to half its original diameter. What happens to the fluid's velocity and pressure in the narrow section compared to the wider section?

Answer: Velocity increases and pressure decreases.

This scenario is explained by the principles of continuity and Bernoulli's equation. The continuity equation (A1*v1 = A2*v2) states that for an incompressible fluid, the product of the cross-sectional area and the velocity must remain constant. When the diameter is halved, the area decreases by a factor of four, so the velocity must increase by a factor of four to maintain a constant flow rate. Bernoulli's principle states that for a horizontal pipe, an increase in fluid speed is accompanied by a decrease in pressure.

A hydraulic lift is used to raise a 2,000 kg car. The piston supporting the car has a surface area of 2.5 m², and the input piston where force is applied has a surface area of 0.1 m². What is the minimum force that must be applied to the input piston to lift the car? (Assume g = 10 m/s²)

Answer: 800 N

This problem is an application of Pascal's Law, which states that a pressure change at any point in a confined incompressible fluid is transmitted throughout the fluid such that the same change occurs everywhere. The pressure on both pistons is equal (P1 = P2). Since Pressure = Force / Area, we have F1/A1 = F2/A2. First, calculate the force exerted by the car (F2), which is its weight: F2 = mass × g = 2,000 kg × 10 m/s² = 20,000 N. Now, solve for the input force (F1): F1 = F2 * (A1 / A2) = 20,000 N * (0.1 m² / 2.5 m²) = 800 N.

Which of the following principles primarily explains why a large steel ship floats on water, while a small steel ball sinks?

Answer: Archimedes' Principle

Archimedes' Principle states that the buoyant force on a submerged object is equal to the weight of the fluid that the object displaces. A ship floats because its large, hollow shape displaces a significant volume of water, creating a buoyant force that is equal to its own weight. A small steel ball, although dense, displaces very little water, so the buoyant force is much less than its weight, causing it to sink.

Viscosity is a measure of a fluid's:

Answer: Resistance to flow

Viscosity is defined as the measure of a fluid's internal friction or its resistance to flow. A fluid with high viscosity, like honey, flows slowly because of the strong internal friction between its layers. A fluid with low viscosity, like water, flows easily.

A river flows from a wide channel into a narrow gorge. According to the principle of continuity, what must happen to the speed of the water as it enters the gorge?

Answer: It increases

The principle of continuity (A1*v1 = A2*v2) states that for an incompressible fluid, the mass flow rate must be constant. As the cross-sectional area (A) of the river channel decreases upon entering the narrow gorge, the velocity (v) of the water must increase to maintain the same volume of water flowing per unit of time.

In a hydraulic system, if a force of 50 N is applied to a small piston with an area of 0.02 m², what is the pressure transmitted throughout the fluid?

Answer: 2,500 Pa

According to Pascal's Law, the pressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid and the walls of the containing vessel. The pressure (P) is calculated as Force (F) divided by Area (A). Therefore, P = 50 N / 0.02 m² = 2,500 Pascals (Pa). This pressure is the same throughout the entire hydraulic system.