In centrifugal pump design, the impeller exit diameter D₂ and speed N (rpm) determine the peripheral velocity U₂ = πD₂N/60. For a pump with D₂ = 300 mm running at 1500 rpm, the peripheral velocity is:
A23.56 m/s
B28.45 m/s
C35.62 m/s
D42.78 m/s
Correct Answer:
A. 23.56 m/s
EXPLANATION
U₂ = π × 0.3 × 1500/60 = 23.56 m/s. This velocity is critical in pump design as it affects the Euler's head and pump efficiency in Indian water supply and irrigation projects.
According to Bernoulli's equation, which energy form is neglected when the fluid flow is at constant elevation in a horizontal pipe?
AKinetic energy
BPotential energy
CPressure energy
DInternal energy
Correct Answer:
B. Potential energy
EXPLANATION
In Bernoulli's equation (P/ρg + V²/2g + Z = constant), when flow is in a horizontal pipe at constant elevation, Z (potential energy head) remains constant and can be neglected in differential form.
The continuity equation for incompressible flow states that A₁V₁ = A₂V₂. If water flows through a pipe that narrows from 100 mm to 50 mm diameter, the velocity ratio V₂/V₁ is:
A1:1
B2:1
C4:1
D1:4
Correct Answer:
C. 4:1
EXPLANATION
Using continuity equation: A₁V₁ = A₂V₂. Area ratio = (D₁/D₂)² = (100/50)² = 4. Therefore V₂/V₁ = 4:1. This is critical for pipe flow analysis in water supply systems.
In fluid mechanics, which of the following statements about Pascal's law is correct?
APressure applied to a confined fluid is transmitted equally in all directions
BPressure decreases with depth in a fluid column
CPressure is inversely proportional to the area of application
DPressure in fluids acts only vertically downward
Correct Answer:
A. Pressure applied to a confined fluid is transmitted equally in all directions
EXPLANATION
Pascal's law states that pressure applied to a confined fluid is transmitted undiminished in all directions. This principle is fundamental to hydraulic systems used in Indian industries.
A 300 mm diameter pipe reduces to 150 mm diameter. If velocity in the larger pipe is 1.5 m/s, what is the velocity in the smaller pipe, assuming incompressible flow?
A3.0 m/s
B6.0 m/s
C9.0 m/s
D12.0 m/s
Correct Answer:
B. 6.0 m/s
EXPLANATION
By continuity equation A₁V₁ = A₂V₂. Since diameter ratio is 2:1, area ratio is 4:1, so V₂ = 1.5 × 4 = 6.0 m/s
A fluid with dynamic viscosity μ = 0.8 Pa·s flows between two parallel plates separated by 5 mm. If the velocity gradient is 100 s⁻¹, what is the shear stress in the fluid?
A80 Pa
B160 Pa
C40 Pa
D320 Pa
Correct Answer:
A. 80 Pa
EXPLANATION
Shear stress τ = μ × (du/dy) = 0.8 × 100 = 80 Pa. This is a direct application of Newton's law of viscosity.
