Day 8 Bernoulli’s Theorem – ECET 2026 Mechanical

Why This Topic is Important for ECET

Bernoulli’s theorem is one of the most fundamental concepts in fluid mechanics. It explains the relation between pressure, velocity, and elevation in a moving fluid. In ECET 2026, this topic is very scoring because questions appear both conceptual (theory) and numerical (applications like venturimeter, orifice meter, pitot tube). Mastering this ensures accuracy in hydraulics questions.

📘 Concept Notes

🔹 Statement of Bernoulli’s Theorem

For a steady, incompressible, non-viscous fluid, along a streamline, the total energy per unit weight remains constant.

This means:

Pressure energy + Kinetic energy + Potential energy = Constant

🔹 Mathematical Form

$\frac{p}{\gamma} + \frac{v^2}{2g} + z = \text{constant}$

where:

ppp = pressure (N/m²)
γ\gammaγ = specific weight (N/m³)
vvv = velocity of fluid (m/s)
ggg = acceleration due to gravity (m/s²)
zzz = elevation head (m)

🔹 Energy Terms in Fluid Flow

Pressure Head → $\frac{p}{\gamma}$
Velocity Head → $\frac{v^2}{2g}$
Elevation Head → $z$

🔹 Assumptions of Bernoulli’s Theorem

Fluid is incompressible.
Fluid flow is steady.
Flow is along a streamline.
No energy loss (ideal conditions).

🔹 Applications of Bernoulli’s Theorem

Venturimeter → measures discharge of fluid.
Orificemeter → measures flow rate.
Pitot tube → measures velocity of fluid.
Nozzle design → high-speed jet applications.
Aircraft wings → lift due to pressure difference.

⚙️ Formulas

Bernoulli’s Equation

$\frac{p_1}{\gamma} + \frac{v_1^2}{2g} + z_1 = \frac{p_2}{\gamma} + \frac{v_2^2}{2g} + z_2$

Continuity Equation

$A_1 v_1 = A_2 v_2$

Discharge through Venturimeter

$Q = C_d A_2 \sqrt{\frac{2gh}{1-(A_2/A_1)^2}}$

Velocity from Pitot Tube

$v = \sqrt{2gh}$

🔟 10 MCQs

Q1. Bernoulli’s theorem is based on the principle of:
a) Conservation of mass
b) Conservation of momentum
c) Conservation of energy
d) Conservation of heat

Q2. In Bernoulli’s equation, $\frac{p}{\gamma}$ term represents:
a) Velocity head
b) Pressure head
c) Elevation head
d) None

Q3. For an ideal fluid flowing in a horizontal pipe of varying diameter, which parameter remains constant?
a) Pressure
b) Velocity
c) Total energy
d) Flow area

Q4. The continuity equation for incompressible fluid is:
a) $A_1 + v_1 = A_2 + v_2$
b) $A_1 v_1 = A_2 v_2$
c) $p_1 = p_2$
d) $z_1 = z_2$

Q5. In a venturimeter, the velocity at throat increases because:
a) Pressure increases
b) Area decreases
c) Friction decreases
d) Density decreases

Q6. The discharge equation of a venturimeter includes:
a) Velocity head only
b) Pressure head only
c) Both velocity and pressure heads
d) Elevation head only

Q7. A pitot tube measures:
a) Pressure only
b) Velocity only
c) Discharge
d) Density

Q8. If velocity doubles in a streamline flow, the kinetic energy head becomes:
a) Half
b) Same
c) Double
d) Four times

Q9. A nozzle works on the principle of:
a) Pascal’s law
b) Bernoulli’s theorem
c) Newton’s law
d) Boyle’s law

Q10. In practical applications, Bernoulli’s theorem is modified to include:
a) Work done
b) Friction losses
c) Momentum changes
d) Heat losses

✅ Answer Key

Q	Ans
1	c
2	b
3	c
4	b
5	b
6	c
7	b
8	d
9	b
10	b

🧠 Explanations

Q1: Bernoulli’s theorem = conservation of energy → (c).
Q2: $\frac{p}{\gamma}$ = pressure head → (b).
Q3: Total energy (sum of heads) remains constant → (c).
Q4: Continuity equation: $A_1 v_1 = A_2 v_2$ → (b).
Q5: At throat, area decreases → velocity increases (continuity principle) → (b).
Q6: Discharge depends on both velocity and pressure heads → (c).
Q7: Pitot tube directly measures velocity → (b).
Q8: KE head $\frac{v^2}{2g}$ . If v doubles → head increases 4 times → (d).
Q9: Nozzle design = Bernoulli’s theorem → (b).
Q10: Real fluids → energy loss due to friction → (b).

🎯 Motivation / Why Practice Matters

Bernoulli’s theorem problems are direct-scoring in ECET 2026.
If you can solve continuity + Bernoulli + venturimeter numericals quickly, you save time for harder questions.
👉 Practicing regularly builds speed, accuracy, and confidence, giving you an edge over others.

📲 CTA

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Day 8 Bernoulli’s Theorem – ECET 2026 Mechanical

Why This Topic is Important for ECET