Questions
6–8 MCQs per paper
Difficulty
Medium-Hard
Importance
High yield for HPCL/NTPC
Overview
Fluid Mechanics and Machinery is a foundational pillar for mechanical engineering, focusing on the behavior of fluids at rest and in motion. It carries significant weight in PSU exams like HPCL, NTPC, and ONGC, testing your analytical ability to solve problems involving hydraulic energy conversion and flow dynamics.
Fluid Properties & Statics
This section covers the fundamental characteristics of fluids such as viscosity, capillarity, and pressure distribution. Mastery of hydrostatic laws is essential as it forms the basis for calculating forces on submerged surfaces.
- Newton's Law of Viscosity: tau = mu * (du/dy)
- Capillary Rise: h = (4 * sigma * cos(theta)) / (rho * g * d)
- Pascal's Law for pressure intensity
- Hydrostatic Law: dP/dz = -rho * g
- Specific gravity: rho_fluid / rho_water
Flow Measurement & Bernoulli's Equation
Bernoulli's equation represents the principle of conservation of energy in fluid flow, vital for analyzing pipeline networks. PSU exams frequently test discharge calculations using flow-measuring devices.
- Bernoulli's Eq: P/rho*g + v^2/2g + z = Constant
- Venturimeter Discharge: Q = Cd * (A1*A2 / sqrt(A1^2 - A2^2)) * sqrt(2g * delta_h)
- Pitot Tube: v = sqrt(2 * g * h_stagnation)
- Energy line vs Hydraulic Gradient line
- Continuity equation: A1*V1 = A2*V2
Laminar & Turbulent Flow
Distinguishing between flow regimes using the Reynolds number is a standard examination requirement. This section emphasizes friction factor calculations and head loss in pipes.
- Reynolds Number (Re) = (rho * v * D) / mu
- Laminar flow: Re < 2000
- Darcy-Weisbach Equation: hf = (f * L * v^2) / (2 * g * D)
- Hagen-Poiseuille equation for pressure drop
- Friction factor (f) for laminar: 64/Re
Hydraulic Turbines & Pumps
This topic deals with energy conversion—turbines convert fluid energy to mechanical work, while pumps do the inverse. Focus on specific speed, efficiency curves, and velocity triangles.
- Specific Speed (Ns) = (N * sqrt(P)) / (H^5/4)
- Pelton wheel is an impulse turbine; Francis/Kaplan are reaction
- Manometric Efficiency of pump: H_m / H_manometric
- Cavitation occurs when pressure falls below vapor pressure
- Work done by jet on plates: rho * A * V * (V - u)
Formula Sheet
tau = mu * (du/dy)
P1/rho*g + v1^2/2g + z1 = P2/rho*g + v2^2/2g + z2 + hL
Q = Cd * A1 * A2 * sqrt(2g*h) / sqrt(A1^2 - A2^2)
Re = rho*v*D/mu
hf = 4*f*L*v^2 / 2*g*D
Ns = N*sqrt(P) / H^0.75 (Turbines)
Ns = N*sqrt(Q) / Hm^0.75 (Pumps)
V = sqrt(2*g*H)
Exam Tip
Always memorize the specific speed ranges and classification of turbines (Pelton vs. Francis vs. Kaplan) as these are direct 'memory-recall' points in every PSU paper.
Common Mistakes
- Mixing up specific speed formulas for pumps and turbines.
- Forgetting to convert units, especially using kinematic viscosity instead of dynamic viscosity.
- Misinterpreting the difference between stagnation pressure and static pressure in Pitot tube problems.
More Revision Notes
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