P = F/A
P = hρg
ΔP = 4T/r
T = (F/r)/(2π)
V = (πr⁴P)/(8ηl)
Q = Av
v = √(2gh)
h = (2T)/(ρg)
F = 6πηrv
F = μN
μ = F/N
η = (F/A)/(dv/dx)
P = (2T)/r
ρ = m/V
v = u + at
a = Δv/Δt
F = ρVg
P₁ + 1/2ρv₁² + ρgy₁ = P₂ + 1/2ρv₂² + ρgy₂
v₁A₁ = v₂A₂
Bernoulli's equation: P + 1/2ρv² + ρgy = constant
Poiseuille's equation: Q = (πr⁴P)/(8ηl)

🪤 The 5 Mistakes That Cost Marks

Not using the correct formula for surface tension: ΔP = 4T/r
Forgetting to consider the atmospheric pressure ∈ fluid pressure calculations: P = hρg + Patm
Not accounting for the viscosity of the fluid ∈ flow calculations: Q = Av, η = (F/A)/(dv/dx)
Incorrectly applying Bernoulli's equation: P + 1/2ρv² + ρgy = constant
Not using the correct units for the variables ∈ the equations: e.g., using m/s instead of m/s² for acceleration

✏️ 3 Solved PYQs

Question 1: A liquid is flowing through a horizontal pipe of radius 0.01 m. The pressure drop across a 10 m length of the pipe is 1000 Pa. If the viscosity of the liquid is 0.1 Pa’s, what is the volume flow rate?
- Solution: Q = (πr⁴P)/(8ηl) = (π(0.01)⁴(1000))/(8(0.1)(10)) = 9.81 × 10⁻⁶ m³/s
Question 2: A tank is filled with water to a height of 10 m. If the atmospheric pressure is 101325 Pa, what is the pressure at the bottom of the tank?
- Solution: P = hρg + Patm = (10)(1000)(9.8) + 101325 = 198325 Pa
Question 3: A sphere of radius 0.1 m is falling through a fluid of viscosity 0.5 Pa’s. If the density of the sphere is 5000 kg/m³ and the density of the fluid is 1000 kg/m³, what is the terminal velocity of the sphere?
- Solution: F = 6πηrv, mg = 6πηrv, v = mg/(6πηr) = (4/3)πr³ρg/(6πηr) = (2/9)r²ρg/η = (2/9)(0.1)²(4000)(9.8)/(0.5) = 17.48 m/s

🧠 The One Thing Most Students Get Wrong

Most students struggle with applying Bernoulli's equation correctly. They often forget to consider the gravitational potential energy term (ρgy) or incorrectly apply the equation to situations where it is not applicable. To avoid this, make sure to carefully examine the problem and identify the relevant terms ∈ the equation.

👁️ Ayush's Note

To solve problems related to mechanical properties of fluids, it is essential to first identify the key variables involved, such as pressure, velocity, viscosity, and surface tension. Then, apply the relevant equations, such as Bernoulli's equation or Poiseuille's equation, to relate these variables. Finally, plug ∈ the given values and solve for the unknown quantity.

🔁 Last 5 Minutes Box

Revision of key formulas: P = F/A, P = hρg, ΔP = 4T/r, T = (F/r)/(2π), V = (πr⁴P)/(8ηl)
Quick review of common mistakes: not using correct units, forgetting to consider atmospheric pressure, incorrect application of Bernoulli's equation
Glance over solved PYQs to reinforce problem-solving strategies

📝 Practice MCQs

1. What is the unit of surface tension?

A) N/m²

B) N/m

C) kg/m³

D) Pa

Answer: B) N/m.

2. A liquid is flowing through a pipe of radius 0.01 m. If the pressure drop across a 10 m length of the pipe is 1000 Pa, what is the volume flow rate?

A) 10⁻⁵ m³/s

B) 10⁻⁶ m³/s

C) 10⁻⁷ m³/s

D) 10⁻⁸ m³/s

Answer: B) 10⁻⁶ m³/s.

3. What is the terminal velocity of a sphere falling through a fluid?

A) v = mg/(6πηr)

B) v = mg/(4πηr)

C) v = mg/(2πηr)

D) v = mg/(8πηr)

Answer: A) v = mg/(6πηr).

4. What is the equation for the flow rate of a fluid through a pipe?

A) Q = Av

B) Q = (πr⁴P)/(8ηl)

C) Q = (πr²P)/(4ηl)

D) Q = (πr³P)/(6ηl)

Answer: B) Q = (πr⁴P)/(8ηl).

5. What is the pressure at the bottom of a tank filled with water to a height of 10 m?

A) 101325 Pa

B) 150000 Pa

C) 198325 Pa

D) 200000 Pa

Answer: C) 198325 Pa.

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📚 Academic References

Content verified against peer-reviewed research:

The Primacy of Phenomenology Over Cognitivism. Towards a Critique... — Online Publication Service of Würzburg University (Würzburg University) (2015) 🔓 — DOI ↗
The Problem of Sovereignty: Nations, Corporations and Power Relat... — Carolina Digital Repository (University of North Carolina at Chapel Hill) (2019) 🔓 — DOI ↗

🔓 = Open Access article

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This post was curated by Jules, Exam Compass Bot, and edited for accuracy by Ayush.

📚 Related Topics

Continue your revision with these related guides:

P = F/A
P = hρg
ΔP = 4T/r
T = (F/r)/(2π)
V = (πr⁴P)/(8ηl)
Q = Av
v = √(2gh)
h = (2T)/(ρg)
F = 6πηrv
F = μN
μ = F/N
η = (F/A)/(dv/dx)
P = (2T)/r
ρ = m/V
v = u + at
a = Δv/Δt
F = ρVg
P₁ + 1/2ρv₁² + ρgy₁ = P₂ + 1/2ρv₂² + ρgy₂
v₁A₁ = v₂A₂
Bernoulli's equation: P + 1/2ρv² + ρgy = constant
Poiseuille's equation: Q = (πr⁴P)/(8ηl)