Top Fluid Mechanics Problems Solved with Examples

Fluid mechanics is a core subject in engineering, covering how liquids and gases move and interact with forces. From water distribution in cities to aircraft wing design, understanding fluid mechanics is essential for safety, efficiency, and innovation.

This guide presents the top fluid mechanics problems solved step by step, with clear explanations and real engineering applications.

Problem 1: Flow Rate in a Pipe (Continuity Equation)

Problem:
A water pipe has a diameter of 0.1 m and carries water at a velocity of 2 m/s. Calculate the flow rate and determine if it is sufficient for residential water distribution.

Step 1: Formula
Q = A × v
where Q = flow rate, A = cross-sectional area, v = velocity.

Step 2: Calculate area
A = π × d² / 4
= π × (0.1²) / 4
= 0.00785 m²

Step 3: Multiply by velocity
Q = 0.00785 × 2
≈ 0.0157 m³/s

Step 4: Interpretation
This equals 15.7 liters per second, enough to supply several homes. Civil engineers use this to ensure pipes deliver adequate water under demand.

Problem 2: Hydrostatic Pressure on a Dam

Problem:
Find the hydrostatic pressure at the bottom of a dam with 20 m water depth. Assume ρ = 1000 kg/m³, g = 9.81 m/s².

Step 1: Formula
P = ρ × g × h

Step 2: Substitute values
P = 1000 × 9.81 × 20
= 196,200 Pa

Step 3: Interpretation
At 20 m depth, the dam wall experiences 196 kN/m² of force. Engineers use this pressure to design safe dam walls with sufficient thickness and reinforcement.

Problem 3: Bernoulli’s Equation in a Pipe

Problem:
Water flows through a pipe that narrows from 0.2 m diameter to 0.1 m. If velocity in the wider section is 1 m/s, find velocity in the narrower section (neglect losses).

Step 1: Apply continuity equation
A₁v₁ = A₂v₂

Step 2: Calculate areas
A₁ = π × (0.2²)/4 = 0.0314 m²
A₂ = π × (0.1²)/4 = 0.00785 m²

Step 3: Solve for v₂
v₂ = (A₁/A₂) × v₁
= (0.0314 / 0.00785) × 1
= 4 m/s

Step 4: Interpretation
Velocity increases 4 times in the narrower section. This principle underlies Venturi meters used in flow measurement.

Problem 4: Lift Force on an Aircraft Wing

Problem:
An aircraft wing has an area of 2 m². Air density = 1.225 kg/m³. Velocity = 50 m/s. Lift coefficient Cl = 1.2. Calculate lift force.

Step 1: Formula
L = 0.5 × ρ × v² × A × Cl

Step 2: Substitute values
L = 0.5 × 1.225 × 50² × 2 × 1.2

= 0.5 × 1.225 × 2500 × 2 × 1.2
= 3675 N

Step 3: Interpretation
The wing generates 3675 N of lift, enough to help balance aircraft weight. Engineers use this in aerodynamic design and stability analysis.

Problem 5: Pump Power Requirement

Problem:
A pump lifts water at Q = 0.05 m³/s to a height of 15 m. Calculate required pump power.

Step 1: Formula
P = ρ × g × Q × h

Step 2: Substitute values
P = 1000 × 9.81 × 0.05 × 15
= 7357.5 W

Step 3: Interpretation
The pump requires 7.36 kW of power (excluding losses). In practice, efficiency is considered (≈70–85%) before motor selection.

Problem 6: Reynolds Number and Flow Type

Problem:
Water flows in a 0.05 m diameter pipe at velocity 1 m/s. Kinematic viscosity ν = 1 × 10⁻⁶ m²/s. Determine if flow is laminar or turbulent.

Step 1: Formula
Re = v × D / ν

Step 2: Substitute values
Re = 1 × 0.05 / (1 × 10⁻⁶)
= 50,000

Step 3: Interpretation
Since Re > 4000, flow is turbulent. This affects pipe friction, energy loss, and pumping cost.

Problem 7: Buoyancy Force on a Submerged Body

Problem:
A block with volume 0.02 m³ is fully submerged in water. Calculate the buoyant force.

Step 1: Formula
F_b = ρ × V × g

Step 2: Substitute values
F_b = 1000 × 0.02 × 9.81
= 196.2 N

Step 3: Interpretation
The block experiences an upward force of 196.2 N. If the block’s weight is less than this, it floats. This principle is essential in ship and submarine design.

Real-World Applications

• Civil Engineering → Water supply, dam design, flood management
• Mechanical Engineering → Pumps, turbines, lubrication, HVAC
• Aerospace Engineering → Lift, drag, propulsion, jet engines
• Environmental Engineering → Wastewater treatment, air pollution modeling
• Marine Engineering → Ship stability, submarine buoyancy

Conclusion

Fluid mechanics is a practical tool that helps engineers design safe, efficient, and sustainable systems. By mastering problems such as flow rate, pressure, lift, buoyancy, and pump power, engineers ensure reliable performance in industries ranging from civil infrastructure to aerospace.