Phys 1011Freshman (1st Year)Engineering & Technology

Fluid Mechanics & Bernoulli's Equation

Continuity equation, Bernoulli's energy theorem, Torricelli's law, and venturi flow meter applications in Ethiopian freshman engineering physics.

MoE National Competency Objectives

State and derive the equation of continuity for incompressible laminar flow.
Derive Bernoulli's equation from the work-energy theorem.
Solve practical problems involving Venturi tubes, Pitot tubes, and siphon flow.
Analyze exit exam level multiple-choice questions on viscous and non-viscous fluid dynamics.

Essential Governing Formulas & Theorems

Continuity Equation

A_1 v_1 = A_2 v_2 = Q = \text{constant}

Q represents volume flow rate in m^3/s for incompressible fluids.

Bernoulli's Energy Equation

P_1 + \frac{1}{2} \rho v_1^2 + \rho g h_1 = P_2 + \frac{1}{2} \rho v_2^2 + \rho g h_2

Applies along a streamline for steady, non-viscous, incompressible flow.

Torricelli's Efflux Velocity

v = \sqrt{2 g h}

Speed of effluent liquid discharging through a small orifice under gravity.

Full step-by-step solutions with theoretical proofs

1 Questions

Q1MoE Freshman Common Exam (Addis Ababa University)

medium

Water flows horizontally through a pipe that narrows from an area of

0.04\text{ m}^2

with velocity

2.0\text{ m/s}

to an area of

0.01\text{ m}^2

. If the pressure in the wider section is

150\text{ kPa}

, what is the pressure in the narrow section? (Assume water density

\rho = 1000\text{ kg/m}^3

)

120 kPa

90 kPa

180 kPa

60 kPa

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