MECHANICAL PROPERTIES OF FLUIDS-QnA

Q1: What is a fluid?

A \(\textbf{fluid}\) is a substance (liquid or gas) that can flow because it cannot resist shear stress permanently and therefore changes shape continuously under an applied tangential force.

Q2: Define pressure in a fluid.

Pressure in a fluid is the normal force exerted per unit area on a surface in contact with the fluid, expressed as \(P = \dfrac{F}{A}\) in SI units of pascal.

Q3: State Pascal’s law for fluids.

Pascal’s law states that any change in pressure applied to an enclosed incompressible fluid is transmitted undiminished and equally in all directions throughout the fluid.

Q4: What is meant by density of a fluid?

Density of a fluid is its mass per unit volume, given by \(\rho = \dfrac{m}{V}\), and for most liquids it remains nearly constant for moderate pressure changes.

Q5: Write the SI unit of surface tension.

The SI unit of surface tension is newton per metre \(\text{(N m}^{-1}\text{)}\), since it is defined as force per unit length acting along the surface of a liquid.

Q6: What is buoyant force?

Buoyant force is the upward force exerted by a fluid on a body wholly or partially immersed in it, equal to the weight of the displaced fluid according to Archimedes’ principle.

Q7: Define streamline (laminar) flow.

Streamline or laminar flow is a steady flow of fluid in which each particle follows a definite smooth path, and the paths of neighboring layers do not intersect.

Q8: What is turbulence in fluid flow?

Turbulence is a type of fluid motion in which the velocity and direction change irregularly with time and position, leading to eddies and chaotic mixing of layers.

Q9: State Bernoulli’s principle in words.

Bernoulli’s principle states that for an incompressible, non-viscous fluid in steady flow, the sum of pressure energy, kinetic energy, and potential energy per unit volume remains constant along a streamline.

Q10: What is viscosity?

Viscosity is the internal friction of a fluid that opposes relative motion between its adjacent layers, arising due to intermolecular forces and momentum transfer between layers.

Q11: Write the expression for pressure at depth \(h\) in a liquid of density \(\rho\).

For a liquid of density \(\rho\) at rest under gravity, the pressure at depth \(h\) below the free surface is \(P = P_{0} + \rho g h\), where \(P_{0}\) is atmospheric pressure.

Q12: What is Reynolds number?

Reynolds number is a dimensionless quantity defined as \(Re = \dfrac{\rho v D}{\eta}\), which characterises the nature of flow and helps predict transition from laminar to turbulent flow.

Q13: Name the device based on Pascal’s law used for lifting heavy vehicles in service stations.

Hydraulic lift (or hydraulic jack) works on Pascal’s law and is widely used in vehicle service stations to raise cars and other heavy loads.

Q14: What is capillary rise?

Capillary rise is the upward movement of a liquid in a narrow tube due to surface tension and adhesive forces between the liquid and tube material.

Q15: Write any one practical application of Bernoulli’s principle.

One application of Bernoulli’s principle is the working of an atomizer or perfume spray, where fast air flow over a tube reduces pressure and draws liquid up as a fine spray.

Q1: State Archimedes’ principle.

Archimedes’ principle states that when a body is wholly or partially immersed in a fluid, it experiences an upward buoyant force equal to the weight of the fluid displaced by the body, which explains floating and sinking.

Q2: Distinguish between absolute pressure and gauge pressure.

Absolute pressure is the total pressure measured relative to perfect vacuum, whereas gauge pressure is the pressure measured above local atmospheric pressure, so absolute pressure equals gauge pressure plus atmospheric pressure.

Q3: Define coefficient of viscosity and write its SI unit.

Coefficient of viscosity is the proportionality constant \(\eta\) in Newton’s law of viscosity, which relates shear stress to the velocity gradient between fluid layers, and its SI unit is pascal-second \(\text{(Pa s)}\).

Q4: What is terminal velocity of a falling sphere in a viscous medium?

Terminal velocity is the constant maximum velocity attained by a body falling through a viscous fluid when the net force becomes zero because viscous drag and buoyant force balance the weight of the body.

Q5: Write any two factors affecting surface tension of a liquid.

Surface tension of a liquid depends mainly on its nature (intermolecular forces) and temperature, generally decreasing with rise in temperature until the critical point.

Q6: Explain why the pressure at the same horizontal level in a fluid at rest is equal.

In a fluid at rest, any difference in pressure at the same horizontal level would cause fluid to flow from high pressure to low pressure until equilibrium is restored, so static fluids maintain equal pressure at a given depth.

Q7: What is hydraulic press? State its principle.

A hydraulic press consists of two pistons of different areas connected by a liquid-filled chamber, and it operates on Pascal’s law so that a small force on the smaller piston produces a large force on the larger piston.

Q8: Differentiate between cohesive and adhesive forces in fluids.

Cohesive forces act between molecules of the same fluid and lead to phenomena like surface tension, whereas adhesive forces act between fluid molecules and solid surfaces and are responsible for wetting and capillarity.

Q9: Give the condition for laminar flow in terms of Reynolds number, and mention its typical critical value for flow in pipes.

Flow is laminar if Reynolds number is below a critical value, usually around \(2000\) for flow in circular pipes, above which the flow gradually becomes turbulent.

Q10: Why does an air bubble rise in water?

An air bubble in water experiences an upward buoyant force equal to the weight of displaced water, while its own weight is smaller, so the net upward force accelerates the bubble upward until it reaches the surface.

Q1: Derive the expression for excess pressure inside a spherical soap bubble due to surface tension.

For a spherical surface in contact with a fluid, surface tension pulls along the surface, creating an inward force that must be balanced by excess internal pressure. Considering a soap bubble with two liquid surfaces, inner and outer, each of radius \(r\), the total inward force due to surface tension is \(2 \times 2\pi r T = 4\pi r T\), where \(T\) is the surface tension. The outward force because of excess pressure \(\Delta P\) across the film acts over the cross-sectional area \(\pi r^{2}\) and equals \(\Delta P \,\pi r^{2}\). Equating the inward and outward forces in equilibrium gives \(\Delta P \,\pi r^{2} = 4\pi r T\). Simplifying, the excess pressure inside the soap bubble becomes \(\Delta P = \dfrac{4T}{r}\), showing that smaller bubbles have larger excess pressure for a given surface tension.

Q2: Explain the working principle of a hydraulic lift and show how a small force can lift a heavy car.

A hydraulic lift uses an incompressible fluid confined between two pistons of different cross-sectional areas and operates on Pascal’s law, which ensures that the pressure is transmitted equally throughout the fluid. If a small force \(F_{1}\) is applied on the narrow piston of area \(A_{1}\), the pressure produced is \(P = \dfrac{F_{1}}{A_{1}}\) and the same pressure acts on the wide piston of area \(A_{2}\), giving an upward force \(F_{2} = P A_{2} = \dfrac{F_{1}A_{2}}{A_{1}}\). Since \(A_{2}\) is much larger than \(A_{1}\), the output force \(F_{2}\) can be many times greater than the applied force, enabling a mechanic to lift a heavy car with a modest effort. Although the force is amplified, energy is conserved because the large piston moves through a smaller distance compared with the motion of the small piston.

Q3: Describe how Bernoulli’s principle explains the lift on an aircraft wing.

An aircraft wing is shaped as an aerofoil so that air flowing over the top surface moves faster than air beneath the wing, creating a difference in dynamic pressure between the two regions. Bernoulli’s principle states that in a streamline flow of an incompressible, non-viscous fluid, regions of higher speed have lower pressure, so the faster flow above the wing leads to reduced pressure compared with the slower flow below. This pressure difference produces an upward resultant force called lift, which can balance the weight of the aircraft when the speed is sufficiently high, thereby keeping the plane in the air during flight.

Q4: Explain the concept of terminal velocity using forces acting on a small sphere falling through a viscous liquid.

When a small sphere is released in a viscous liquid, its weight initially exceeds the upward forces and it accelerates downward under gravity. As its speed increases, the viscous drag given approximately by Stokes’ law \(F_{v} = 6\pi \eta r v\) for low Reynolds number also increases, while the buoyant force equal to the weight of displaced liquid remains constant. Eventually, the drag and buoyant force together balance the weight of the sphere, making the net force zero, so the sphere then falls with a constant speed known as terminal velocity. The value of this terminal velocity depends on the radius and density of the sphere, the density of the liquid, and its coefficient of viscosity.

Q5: What is capillary action? Discuss one daily-life example illustrating its importance.

Capillary action is the rise or fall of a liquid in a narrow tube or porous material due to the combined effect of surface tension, cohesion within the liquid, and adhesion between the liquid and the solid surface. When adhesive forces between the liquid and the tube are stronger than cohesive forces, the liquid climbs up the walls, producing a concave meniscus and rising above the surrounding level, as happens with water in glass capillaries. A common example is the upward movement of water in the tiny vessels of plants; capillary action helps draw water from the soil through fine xylem tubes towards the leaves, supporting essential processes like photosynthesis and transpiration.

Q1: Discuss the role of viscosity in blood flow through human arteries and veins.

Blood is a complex fluid whose viscosity plays a crucial role in determining how easily it flows through arteries, veins, and capillaries in the circulatory system. When viscosity becomes abnormally high, the heart must work harder to maintain the same flow rate, increasing cardiovascular strain and potentially contributing to health issues such as hypertension. On the other hand, if blood becomes too thin, clotting may be less effective and internal bleeding risk can rise, so the body maintains viscosity within a narrow range by regulating factors like plasma proteins and temperature. Understanding viscosity and laminar versus turbulent flow also helps in designing medical devices such as artificial heart valves and catheters so that they minimise damage to blood cells and avoid the formation of dangerous clots.

Q2: How does Bernoulli’s equation embody the principle of energy conservation in fluid flow? Explain with an example from everyday life.

Bernoulli’s equation combines pressure energy, kinetic energy, and potential energy per unit volume into a single constant along a streamline, mirroring the conservation of mechanical energy for a non-viscous, incompressible fluid in steady motion. When fluid speeds up in a narrow region of a pipe, its kinetic energy per unit volume increases, so the sum can remain constant only if either pressure or height decreases, which is why pressure is lower in constricted sections. A practical example is the working of a Venturi meter used to measure flow rate; fluid entering a narrow throat speeds up and experiences a pressure drop, and by comparing the pressures at the wide and narrow sections, the device calculates the discharge through the pipe. Another everyday example is the reduced pressure above a moving train, which can draw loose objects towards it, highlighting how energy conservation governs pressure variations in fast-moving fluids.

Q3: Describe how surface tension leads to the spherical shape of small liquid drops and discuss factors that can change this behaviour.

Surface tension tends to minimise the surface area of a liquid for a given volume because molecules at the surface have higher potential energy than those inside, so the system favours configurations with fewer exposed molecules. For an isolated drop, the shape with the smallest area for a fixed volume is a sphere, so tiny droplets of water or oil in air naturally become nearly spherical when gravitational and other external forces are weak. The value of surface tension decreases with increase in temperature and can be altered by adding impurities or surfactants such as detergents, which reduce cohesive forces at the surface; as a result, warm water with soap forms drops that are more easily deformed and spread out rather than remaining perfectly spherical.

Q4: Explain how the continuity equation is derived for incompressible fluids and discuss one application of this principle.

The continuity equation arises from conservation of mass in fluid flow: for an incompressible fluid, the mass passing through one cross-section of a tube in a given time must equal the mass passing through any other cross-section in the same time. If \(A_{1}\) and \(A_{2}\) are the areas of two sections of a pipe and \(v_{1}\) and \(v_{2}\) are the corresponding flow speeds, then \(\rho A_{1}v_{1} = \rho A_{2}v_{2}\), which simplifies to \(A_{1}v_{1} = A_{2}v_{2}\) when the density \(\rho\) is constant. This relation explains why water from a garden hose speeds up when the nozzle is partially closed: the reduced area of exit forces the fluid to move faster so that the volume flow rate remains the same, allowing the jet to reach farther distances.

Q5: Discuss in detail how the concepts of pressure, buoyancy, and density together determine whether a body floats or sinks in a fluid.

Whether a body floats or sinks depends on the interplay between its weight, which is the gravitational force acting downward, and the buoyant force exerted upward by the displaced fluid. The weight of the body equals \(W = \rho_{b} V g\), where \(\rho_{b}\) is the average density of the body and \(V\) its volume, while the buoyant force equals \(\rho_{f} V_{d} g\), with \(\rho_{f}\) the fluid density and \(V_{d}\) the volume of displaced fluid; for a fully submerged body \(V_{d} = V\). If the body’s density is greater than that of the fluid, its weight exceeds the buoyant force and it sinks, whereas if its density is smaller, it can float with only part of its volume submerged so that the displaced fluid’s weight matches its own. Pressure in the surrounding fluid increases with depth, generating a net upward force on the bottom of the body, and designers of ships and submarines exploit this by adjusting shape and internal volume so that effective density and displacement create the desired floating or diving behaviour.