EIT - Engineer In Training Fluid Mechanics Questions and Answers — Questions and Answers
Question 1: Water flows through a horizontal pipe that transitions from a diameter of 10 cm to a diameter of 5 cm. If the velocity in the 10 cm section is 1.5 m/s, what is the approximate velocity in the 5 cm section, assuming incompressible flow?
- 0.75 m/s
- 3.0 m/s
- 6.0 m/s (Correct answer)
- 0.375 m/s
Correct answer: 6.0 m/s
This problem is solved using the principle of conservation of mass, expressed by the continuity equation for incompressible fluids: A₁v₁ = A₂v₂. Here, A is the cross-sectional area and v is the velocity. The area of a circular pipe is A = π(D/2)². Substituting this into the continuity equation gives (πD₁²/4)v₁ = (πD₂²/4)v₂. The π/4 terms cancel, leaving D₁²v₁ = D₂²v₂. Solving for v₂ gives v₂ = v₁ * (D₁/D₂)². Plugging in the given values: v₂ = 1.5 m/s * (10 cm / 5 cm)² = 1.5 m/s * (2)² = 1.5 m/s * 4 = 6.0 m/s.
Question 2: A 0.5 m³ block of wood with a specific gravity of 0.7 is held fully submerged in freshwater (density ≈ 1000 kg/m³). What is the magnitude of the buoyant force acting on the block? (Use g = 9.81 m/s²)
- 3434 N
- 4905 N (Correct answer)
- 6867 N
- 500 N
Correct answer: 4905 N
According to Archimedes' principle, the buoyant force is equal to the weight of the fluid displaced by the object. The volume of fluid displaced is equal to the volume of the submerged object, which is 0.5 m³. The buoyant force (Fb) is calculated as Fb = ρ_fluid * g * V_submerged. Using the given values: Fb = (1000 kg/m³) * (9.81 m/s²) * (0.5 m³) = 4905 N. The specific gravity of the block itself is not needed to calculate the buoyant force when the submerged volume is known.
Question 3: In fluid mechanics, the Reynolds number (Re) is a dimensionless quantity used to predict flow patterns. Which of the following statements is most accurate regarding flow in a pipe?
- It is the ratio of viscous forces to inertial forces.
- A Reynolds number below 2300 typically indicates turbulent flow.
- It is directly proportional to the fluid's kinematic viscosity.
- It represents the ratio of inertial forces to viscous forces. (Correct answer)
Correct answer: It represents the ratio of inertial forces to viscous forces.
The Reynolds number is a fundamental dimensionless quantity in fluid mechanics that represents the ratio of inertial forces to viscous forces within a fluid. For pipe flow, a Reynolds number less than approximately 2300 indicates laminar flow, while a value greater than about 4000 indicates turbulent flow. The range between these values is considered transitional. The formula Re = (ρvD)/μ shows it is inversely proportional to dynamic viscosity (μ) and kinematic viscosity (ν = μ/ρ).
Question 4: Water flows from a large-diameter pipe into a smaller-diameter pipe at the same elevation. Assuming no frictional losses, which of the following occurs?
- Both the fluid velocity and pressure increase.
- The fluid velocity increases and the pressure decreases. (Correct answer)
- The fluid velocity decreases and the pressure increases.
- Both the fluid velocity and pressure decrease.
Correct answer: The fluid velocity increases and the pressure decreases.
This scenario is explained by two key principles. First, the continuity equation (A₁v₁ = A₂v₂) dictates that as the pipe area (A) decreases, the fluid velocity (v) must increase to maintain a constant flow rate. Second, Bernoulli's principle for a horizontal pipe (P + ½ρv² = constant) states that where velocity is higher, pressure (P) must be lower to conserve energy. Therefore, as the water enters the narrower pipe, its velocity increases and its static pressure decreases.
Question 5: A vertical rectangular gate in a dam is 2 meters wide and 3 meters high, and its top edge is 4 meters below the water surface. What is the total hydrostatic force acting on the gate? (Use ρ_water = 1000 kg/m³, g = 9.81 m/s²)
- 176.6 kN
- 235.4 kN
- 264.9 kN (Correct answer)
- 323.7 kN
Correct answer: 264.9 kN
The total hydrostatic force on a submerged plane surface is the product of the pressure at the centroid of the surface and the area of the surface (F = P_c * A). The area of the gate is A = 2 m * 3 m = 6 m². The centroid of the rectangular gate is at its geometric center, which is 3/2 = 1.5 m down from its top edge. The vertical depth to the centroid (h_c) is the depth of the top edge plus the distance to the centroid: h_c = 4 m + 1.5 m = 5.5 m. The pressure at the centroid is P_c = ρ * g * h_c = 1000 kg/m³ * 9.81 m/s² * 5.5 m = 53955 Pa. The total force is F = 53955 Pa * 6 m² = 323730 N, or approximately 323.7 kN.
Question 6: A U-tube manometer filled with mercury (SG = 13.6) is used to measure the gauge pressure of a gas. The mercury level on the side open to the atmosphere is 15 cm higher than the level on the side connected to the gas. What is the gauge pressure of the gas? (Use ρ_water = 1000 kg/m³, g = 9.81 m/s²)
- 20.0 kPa (Correct answer)
- 14.7 kPa
- 1.47 kPa
- 133.4 kPa
Correct answer: 20.0 kPa
The gauge pressure is the pressure difference indicated by the height difference of the manometer fluid. The pressure difference (ΔP) is calculated using the formula ΔP = ρ_fluid * g * Δh. First, calculate the density of mercury: ρ_mercury = SG * ρ_water = 13.6 * 1000 kg/m³ = 13600 kg/m³. The height difference (Δh) must be in meters: 15 cm = 0.15 m. Now, calculate the pressure: ΔP = (13600 kg/m³) * (9.81 m/s²) * (0.15 m) = 20012.4 Pa, which is approximately 20.0 kPa. Since the atmospheric side is higher, the gas pressure is above atmospheric pressure by this amount.
EIT - Engineer In Training Fluid Mechanics Questions and Answers
Water flows through a horizontal pipe that transitions from a diameter of 10 cm to a diameter of 5 cm.
If the velocity in the 10 cm section is 1.5 m/s, what is the approximate velocity in the 5 cm section, assuming incompressible flow?