INPHO Fluid Mechanics Questions, Practice Problems with Detailed Solutions

INPHO Fluid Mechanics Questions cover a vital branch of physics that is crucial for competitive exams like the Indian National Physics Olympiad. This field involves the study of fluids (liquids and gases) under various conditions, covering both static and dynamic aspects. Because these questions often blend multiple complex concepts, they demand strong analytical and problem-solving skills from students. Mastering this area is essential for aspirants who are aiming to excel in advanced physics competitions and secure top ranks.

Here we have discussed essential INPHO Fluid Mechanics practice questions, complete with detailed answers. Students will gain insights into question patterns, learn effective problem-solving strategies, and reinforce their conceptual understanding. This resource helps students prepare for the rigor of INPHO Fluid Mechanics numerical problems and improve their overall exam readiness.

Also Read: INPhO Syllabus

Important NPHO Fluid Mechanics Questions

This section presents a curated set of important INPHO Fluid Mechanics questions covering various difficulty levels and types, from single-correct to subjective problems. These questions help in assessing and enhancing your understanding of key fluid mechanics principles.

Question 1: Single Correct

Problem: A liquid jet of velocity v and area A strikes a fixed hollow cone, as shown in the figure, and deflects back as a conical sheet at the same speed. Find the angle θ for which the restraining force
F = (3/2) ρ A v²
(where ρ is the density of the liquid).

(A) 30°
(B) 45°
(C) 60°
(D) 15°

Answer: (C) 60°

Question 2: Multiple Correct

Problem: A small source of light is mounted inside a cylindrical container of height h. The bottom of the container is covered with a mirror. Initially, the container is empty. Then a clear liquid with refractive index n is slowly poured into the container. The level of liquid H rises steadily, reaching the top of the container in time T. Let h₁ be the distance of the source of light from the bottom of the container. Consider paraxial ray approximation and two cases:
(1) H ≤ h₁
(2) h₁ ≤ H ≤ h

Options:
(A) The speed of the image of the source in case (1) during this process is (2h/T)(1 − 1/n)
(B) The speed of the image of the source in case (2) during this process is (h/T)(1 − 1/n)
(C) The speed of the image of the source in case (1) during this process is (h/2T)(1 − 1/n)
(D) The speed of the image of the source in case (2) during this process is (h/2T)(1/n)

Answer: (A, B)

Question 3: Multiple Correct

Problem: Two spherical soap bubbles in vacuum are connected through a narrow tube. The radius of the left bubble is R and that of the other is slightly smaller than R. Air flows from right to left very slowly. At any instant r, A, V, n are radius, surface area, volume, and number of moles of gas. Suppose at some instant the number of moles in the left bubble is 4 times the number of moles in the right bubble. Select the CORRECT statement(s):

(A) r₂ = R √(2/5)
(B) r₁ = R √(8/5)
(C) A₁ + A₂ = constant
(D) V₁ + V₂ = constant

Answer: (A, B, C)

Question 4: Integer Type

Problem: A soap film is formed between two square figures made of a uniform wire. The bigger square is held in a horizontal plane and the smaller square is slowly allowed to drop vertically. It reaches equilibrium after dropping a height h. Let surface tension = T, mass per unit length of wire = λ, and acceleration due to gravity = g. Given that:

h = (n λ g a) / [2 √(4T² − λ² g²)]

Find the integer value n.

Answer: 3

Question 5: Subjective Type

Problem: Two very large open tanks A and F contain the same liquid. A horizontal pipe BCD has a constriction at C. A vertical pipe E containing air opens into the constriction at C and dips into the liquid in tank F. If the cross-sectional area at C is one-half that at D, and D is at a distance h₁ below the liquid level in A, to what height h₂ will liquid rise in pipe E?

Solution: The height h₂ is 3h₁.

Question 6: Subjective / Analytical

Problem: In a dense fog, a water drop sinks and absorbs smaller drops in its path. It is found to be accelerating uniformly despite air drag proportional to the square of the speed (v²) and cross-sectional area (r²). What is the maximum possible value for this acceleration?

Solution Summary:
The radius of the drop grows proportional to the distance x:
r(x) = (1/4)(ρ_fog / ρ_water) x

The mass rate of change is:
dm/dx = 3m/x

Using Newton’s second law:
d(mv)/dt = mg − drag

Substituting v = √(2ax) for uniform acceleration:

a = g / [7 + 3 c_d ρ_air / ρ_fog]

In the limiting case where ρ_fog ≫ ρ_air, the maximum acceleration is:
a < g/7

Answer: g/7

INPHO Fluid Mechanics Questions PDF Library

Mastering fluid statics and dynamics requires consistent practice with high-level problems. To assist your preparation, we have compiled comprehensive resources including previous year papers and curated practice sets. Use the links below to download the INPHO Fluid Mechanics questions PDF and start solving advanced numerical problems designed by Olympiad experts.

How to Use Important Solutions for INPHO Fluid Mechanics for Exam Preparation?

Effective use of these solved INPHO Fluid Mechanics questions can significantly boost your exam preparation. Follow these steps to maximize your learning and readiness.

• Master Concepts First: Before attempting the problems, ensure a solid understanding of fluid statics, dynamics, Bernoulli's principle, and surface tension.

• Attempt Problems Independently: Try to solve each problem on your own first. This practice identifies areas where you need more clarity or understanding.

• Analyze Solved Questions: Compare your solutions with the provided answers. Understand the steps and reasoning, especially for challenging inpho fluid mechanics solved questions.

• Identify Weak Areas: Pay attention to problems you struggled with. Revisit the concepts related to those problems for deeper learning.

• Practice Advanced Problems: These inpho fluid mechanics practice questions are designed for high-level exams. Regular practice builds confidence and problem-solving speed.

• Review Regularly: Use these solutions for quick revision of complex topics and common question types before the exam.