Practice Questions

Name the principle that explains the operation of hydraulic machines like a hydraulic lift.

Justify why pressure in a fluid is a scalar quantity, even though it is defined as force per unit area, and force is a vector.

Water flows through a horizontal pipe of non-uniform cross-section. At a point where the radius of the pipe is $2.0$ cm, the velocity of water is $3.0 \text{ m/s}$. Calculate the velocity of water at a point where the radius is $1.0$ cm.

Justify why a liquid drop, free from external forces like gravity, assumes a spherical shape.

A large open tank has a small hole at a depth of $5.0$ m from the surface of the water. Apply Torricelli's law to calculate the speed of efflux of water from the hole. (Use $g = 9.8 \text{ m/s}^2$)

Define pressure and identify its SI unit.

Examine why blowing over a piece of paper held horizontally under your lip causes the paper to rise.

Recall the mathematical formula for the gauge pressure at a depth $h$ below the surface of a liquid with density $\rho$.

Calculate the excess pressure inside a soap bubble of radius $4.00$ mm. The surface tension of the soap solution is $2.50 \times 10^{-2} \text{ N/m}$.

Explain why the pressure in a fluid at rest is the same at all points located at the same horizontal level.

Identify the property of a fluid that is responsible for the internal resistance to its flow.

Define the term 'angle of contact' as it relates to a liquid surface in contact with a solid.

State Bernoulli's principle and write its mathematical equation.

Describe the key differences between streamline flow and turbulent flow of a fluid.

State the equation of continuity for an incompressible fluid in steady flow and explain what physical principle it represents. Describe how the speed of the fluid changes as it flows through a pipe of varying cross-section.

State and explain Pascal's law. Describe with the help of a diagram how this law is applied in a hydraulic lift.

Analyze why a small drop of liquid, free from external forces like gravity, assumes a spherical shape.

A 50 kg person stands on a single circular stiletto heel of radius $0.5$ cm. A circus performer has a 50 kg plank placed on their chest, and a 5000 kg elephant stands on the plank. The performer is unharmed. Critique the physics that explains the performer's safety, and formulate a calculation to compare the pressure in both scenarios.

Explain the phenomenon of capillary rise. Recall the expression for the height to which a liquid rises in a capillary tube and list the factors on which this height depends.

A cylindrical block of mass $25$ kg and base radius $5$ cm rests on a horizontal floor. Calculate the pressure the block exerts on the floor. (Use $g = 9.8 \text{ m/s}^2$)

In a hydraulic lift, the radius of the smaller piston is $4.0$ cm and that of the larger piston is $20.0$ cm. Calculate the force that must be applied to the smaller piston to lift a car of mass $1500$ kg. (Use $g = 10 \text{ m/s}^2$)

Analyze the effect of temperature on the viscosity of fluids. Contrast the behavior of liquids and gases when their temperature increases.

Calculate the height to which water will rise in a glass capillary tube of radius $0.25$ mm. (Surface tension of water $S = 0.0727 \text{ N/m}$, density of water $\rho = 1000 \text{ kg/m}^3$, angle of contact $\theta = 0^\circ$, and $g = 9.8 \text{ m/s}^2$)

Critique the statement: "Bernoulli's principle applies to all instances of fluid motion." Justify your assessment by discussing the key assumptions made in its derivation.

Propose a design for a hydraulic lift system that uses Pascal's law to lift a $2000$ kg vehicle using a maximum input force of only $500$ N. Formulate the required ratio of the piston areas and justify your design choice.

An engineer is designing an open-tube manometer to measure pressure differences in a gas line. Propose which liquid, mercury or colored water, should be used for measuring (a) very small pressure differences and (b) large pressure differences. Justify your proposals.

Evaluate the two diagrams shown in Exercise 9.15 of the source document. Justify which diagram correctly represents the steady flow of a non-viscous liquid and why the other is incorrect.

A student claims that the formula for capillary rise, $h = \frac{2S \cos\theta}{a\rho g}$, can be used to calculate the height change for any liquid in any capillary tube. Critique this claim, specifically for the case of mercury in a clean glass tube.

A submarine is at a depth of $500$ m. The interior is maintained at sea-level atmospheric pressure. Propose a method to calculate the net force on a circular viewport of radius $0.2$ m. Justify your steps and perform the calculation. (Use density of seawater $\rho = 1.03 \times 10^3 \text{ kg/m}^3$, $P_a = 1.01 \times 10^5 \text{ Pa}$, and $g = 9.8 \text{ m/s}^2$).

A submarine is at a depth of $500$ m in the ocean. Calculate the gauge pressure and the absolute pressure at this depth. (Density of sea water $\rho = 1.03 \times 10^3 \text{ kg/m}^3$, atmospheric pressure $P_a = 1.01 \times 10^5 \text{ Pa}$, and $g = 10 \text{ m/s}^2$)

Compare the pressure at the top and bottom surfaces of an airplane wing during flight and analyze how this difference generates lift, using Bernoulli's principle.

Formulate a scientific explanation for why adding detergent to water enhances its ability to clean greasy fabrics. Your explanation must be based on the concepts of surface tension and angle of contact.

Justify why it is more effective to control the flow rate of an injection using the size of the syringe needle rather than the thumb pressure exerted.

Calculate the terminal velocity of a steel ball of radius $2.0$ mm falling through glycerine. (Density of steel $\rho = 8.0 \times 10^3 \text{ kg/m}^3$, density of glycerine $\sigma = 1.3 \times 10^3 \text{ kg/m}^3$, viscosity of glycerine $\eta = 0.83 \text{ Pa s}$, and $g = 9.8 \text{ m/s}^2$)

Explain the concepts of surface tension and surface energy. Summarize the steps to show the relationship between the force due to surface tension and the surface energy per unit area for a liquid film.

Design a simple experiment to determine the coefficient of viscosity of honey using Stokes' law. Formulate the necessary equation and evaluate two potential sources of significant error in your proposed method.

A swimmer is at a depth of $10 \text{ m}$ below the surface of a lake. Recall the formula for absolute pressure and calculate its value. Use atmospheric pressure $P_a = 1.01 \times 10^5 \text{ Pa}$, density of water $\rho = 1000 \text{ kg/m}^3$, and acceleration due to gravity $g = 9.8 \text{ m/s}^2$.

Examine the hydrostatic paradox. Why does the force on the bottom of three vessels with the same base area and filled to the same height with a liquid remain the same, even if the vessels hold different amounts of liquid?

Evaluate the common explanation that the curve of a spinning cricket ball (Magnus effect) is due to the pressure difference predicted by Bernoulli's principle. Justify whether this principle alone is sufficient to explain the phenomenon.

Explain the concept of viscosity. Define the coefficient of viscosity, and state its SI unit and dimensions. Summarize how the viscosity of liquids and gases changes with temperature.

Propose the pressure required to blow a hemispherical bubble of radius $2.0$ mm at the end of a capillary tube dipped $10.0$ cm below the surface of a soap solution. The surface tension of the solution is $2.50 \times 10^{-2} \text{ N/m}$, its density is $1.20 \times 10^3 \text{ kg/m}^3$, and atmospheric pressure is $1.01 \times 10^5 \text{ Pa}$. Justify your formula for the total pressure.

Explain, using the concept of surface energy, why a small liquid drop under no external forces assumes a spherical shape.

Analyze the motion of a spinning cricket ball in air to explain why it deviates from a parabolic path. Apply Bernoulli's principle in your explanation.

A horizontal pipe carries water in a streamline flow. At a point along the pipe where the cross-sectional area is $10 \text{ cm}^2$, the water velocity is $1 \text{ m/s}$ and the pressure is $2000$ Pa. Calculate the pressure at another point where the cross-sectional area is $5 \text{ cm}^2$. The density of water is $1000 \text{ kg/m}^3$.

Design an experiment to verify Bernoulli's principle for a horizontal pipe of varying cross-section. Justify your choice of apparatus, outline the procedure, and formulate the relationship you would expect to observe between pressure and velocity.