CELE Hydraulics & Fluid Mechanics — Hydrodynamics and Fluid MachineryConcept Map

Concept

Force of a Jet (Momentum Principle)

Sub Concepts

• Momentum equation: ΣF = ρQ(v_out − v_in)
• Flat plate normal impact: F = ρQv = ρAv²
• Inclined plate: F_n = ρQv sin(α)
• Curved vane turning by angle θ: F_x = ρQv(1 − cos θ)
• Relative velocity for moving vanes: (v − u)
• Discharge calculation: Q = Av

Relationship To Central

Foundation for analyzing dynamic forces in fluid systems

Concept

Force on Pipe Bends

Sub Concepts

• Component momentum forces: F_x, F_y
• Pressure forces at inlet and outlet: p₁A₁, p₂A₂
• Vector addition: ΣF_x = ρQ(v_2x − v_1x) + (p₁A₁)_x − (p₂A₂)_x
• Resultant anchoring force: √(F_x² + F_y²)
• Pipe support and restraint design
• Anchor bolt and saddle calculations

Relationship To Central

Application of momentum principle to structural design

Concept

Pumps (Energy Addition)

Sub Concepts

• Pump head H (total dynamic head)
• Water power (output): P_water = γQH
• Input (shaft) power: P_input = γQH/η
• Pump efficiency η (0.70–0.90 typical range)
• Affinity laws: Q ∝ N, H ∝ N², P ∝ N³
• Net Positive Suction Head (NPSH) and cavitation
• Types: centrifugal, reciprocating, gear pumps
• Motor power selection and speed matching

Relationship To Central

Devices that add mechanical energy to fluid flow

Concept

Turbines (Energy Extraction)

Sub Concepts

• Turbine net head H
• Power output: P_output = η·γ·Q·H
• Turbine efficiency η (0.85–0.95 typical range)
• Impulse turbines: Pelton wheel (high head, low flow)
• Reaction turbines: Francis (mixed), Kaplan (low head, high flow)
• Specific speed and turbine selection
• Governor and speed regulation
• Runner and blade design

Relationship To Central

Devices that extract mechanical energy from fluid flow

Concept

Power and Head Relationships

Sub Concepts

• Specific weight γ = 9.81 kN/m³ (for SI)
• Density ρ = 1000 kg/m³ (water)
• Power units: kW, MW, hp
• Head in metres (m)
• Flow rate Q in m³/s or L/s
• Conversion between power and head
• Energy balance in open channels and pipes

Relationship To Central

Quantitative analysis of energy transfer in fluid machinery

Concept

Affinity Laws (Pump and Turbine Scaling)

Sub Concepts

• Speed relationship: N₁/N₂
• Discharge law: Q₁/Q₂ = N₁/N₂
• Head law: H₁/H₂ = (N₁/N₂)²
• Power law: P₁/P₂ = (N₁/N₂)³
• Constant geometry assumption
• Application to rpm changes (e.g., 1450 to 1750 rpm)
• Limitation: similar flow regimes

Relationship To Central

Predict performance changes with speed variation

Concept

Cavitation and NPSH

Sub Concepts

• Vapor pressure of water (temperature-dependent)
• Available NPSH: H_a = P_atm/γ − h_s − h_f − P_v/γ
• Required NPSH: H_r (manufacturer specification)
• Cavitation damage: pitting, noise, vibration
• Pump placement (flooded suction vs. lifting)
• Suction lift and atmospheric pressure
• Protection measures and system design

Relationship To Central

Critical constraint on pump suction performance

Concept

Numerical Problem-Solving Strategy

Sub Concepts

• Step 1: Identify system type (jet, bend, pump, turbine)
• Step 2: Select governing equation (momentum, energy, affinity)
• Step 3: Identify known and unknown quantities
• Step 4: Apply SI unit consistency (m, m³/s, kW, kN)
• Step 5: Perform calculation with proper significant figures
• Step 6: Verify answer reasonableness and units
• Step 7: Explain physical meaning of result

Relationship To Central

Systematic approach to licensure-exam problems

To

Force of a Jet

From

Momentum Principle

Strength

strong

Relationship

Fundamental law: ΣF = ρQ(v_out − v_in) governs all jet-impact forces

To

Curved Vane

From

Force of a Jet

Strength

strong

Relationship

Vane deflects jet through angle θ, reducing exit velocity and amplifying force

To

Momentum Principle

From

Force on Pipe Bends

Strength

strong

Relationship

Momentum equations in x and y directions applied to fluid in pipe

To

Water Power

From

Pump Head H

Strength

strong

Relationship

Water power P_w = γQH directly proportional to head added by pump

To

Input Power

From

Pump Efficiency

Strength

strong

Relationship

Input power = γQH/η; dividing by efficiency accounts for mechanical losses

To

Power Output

From

Turbine Head H

Strength

strong

Relationship

Power output = η·γ·Q·H; turbine efficiency multiplies available water power

To

Pump Performance

From

Affinity Laws

Strength

strong

Relationship

Speed changes scale discharge (Q∝N), head (H∝N²), and power (P∝N³)

To

Turbine Performance

From

Affinity Laws

Strength

strong

Relationship

Same scaling laws apply; predict turbine output when speed varies

To

NPSH

From

Cavitation

Strength

strong

Relationship

Cavitation occurs when local pressure drops below vapor pressure; NPSH margin prevents this

To

NPSH Available

From

Vapor Pressure

Strength

moderate

Relationship

Available NPSH decreases as temperature increases (vapor pressure rises)

To

NPSH Available

From

Suction Lift

Strength

strong

Relationship

Lifting water from a source reduces available NPSH; flooded suction improves it

To

Affinity Laws

From

Pump Type Selection

Strength

moderate

Relationship

Centrifugal pumps follow affinity laws; reciprocating pumps do not

To

Jet Force Principle

From

Impulse Turbine (Pelton)

Strength

strong

Relationship

Pelton bucket deflects jet; force comes from momentum change of water

To

Pressure Head Conversion

From

Reaction Turbine (Francis, Kaplan)

Strength

moderate

Relationship

Reaction turbines convert both pressure and velocity energy in submerged runner

To

Power Calculations

From

Specific Weight γ

Strength

strong

Relationship

γ = 9.81 kN/m³ is constant for freshwater; used in P = γQH formula

To

Momentum Force

From

Density ρ

Strength

strong

Relationship

ρ = 1000 kg/m³ for water; used in F = ρQv formula for jet forces

To

Power Calculations

From

Discharge Q

Strength

strong

Relationship

Power is proportional to Q; doubling flow doubles power (at constant head)

To

Moving Vane Force

From

Relative Velocity

Strength

strong

Relationship

Force on moving vane depends on (v − u), not absolute jet velocity

To

Pipe Bend Anchoring

From

Pressure Force

Strength

strong

Relationship

Pressure forces p₁A₁ and p₂A₂ contribute significantly to anchor load

To

Resultant Bend Force

From

Vector Addition

Strength

strong

Relationship

Resultant = √(F_x² + F_y²); direction found using atan2(F_y, F_x)