Fluid flash cards

1. 1.Define pressure exerted by a fluid and state its SI unit.

   Pressure is the normal force exerted per unit area: $P = \dfrac{F}{A}$. SI unit is pascal (Pa), where $1\ \text{Pa} = 1\ \text{N m}^{-2}$. It is a scalar quantity.

   Hint: Force per unit area.

2. 2.Why is fluid pressure a scalar even though force is a vector?

   At a point in a fluid at rest, pressure acts equally in all directions. The force it produces on any surface is always normal to that surface, so pressure itself has no unique direction — it is a scalar.

   Hint: Same in all directions at a point.

3. 3.State how pressure varies with depth in a static liquid.

   $P = P_0 + \rho g h$, where $P_0$ is pressure at the top surface, $\rho$ the liquid density, and $h$ the depth. Pressure increases linearly with depth.

   Hint: Add $\rho g h$ to the surface pressure.

4. 4.Distinguish gauge pressure from absolute pressure.

   Gauge pressure is the excess over atmospheric: $P_{gauge} = P - P_{atm} = \rho g h$. Absolute pressure is the total: $P_{abs} = P_{atm} + \rho g h$.

   Hint: Gauge = absolute minus atmospheric.

5. 5.What is the value of 1 atmosphere in pascals and in terms of a mercury column?

   $1\ \text{atm} = 1.013\times10^5\ \text{Pa}$, which supports a column of mercury $76\ \text{cm}$ (0.76 m) high.

   Hint: About $10^5$ Pa; 76 cm of Hg.

6. 6.Explain the working principle of a mercury barometer.

   Atmospheric pressure supports a mercury column in an inverted tube; the column height $h$ gives $P_{atm} = \rho_{Hg} g h$. The space above mercury (Torricellian vacuum) has ~zero pressure.

   Hint: Torricelli: atmosphere balances a Hg column.

7. 7.Why is mercury preferred over water in a barometer?

   Mercury's high density ($13.6\times10^3\ \text{kg m}^{-3}$) keeps the column short (~76 cm); a water barometer would need a column about $10.3\ \text{m}$ tall. Mercury also has low vapour pressure.

   Hint: High density → short column.

8. 8.State Pascal's law.

   A change in pressure applied to an enclosed incompressible fluid is transmitted undiminished to every point of the fluid and to the walls of the container.

   Hint: Pressure change is transmitted equally throughout.

9. 9.How does a hydraulic lift use Pascal's law to multiply force?

   Equal pressure on both pistons gives $\dfrac{F_1}{A_1} = \dfrac{F_2}{A_2}$, so $F_2 = F_1\dfrac{A_2}{A_1}$. A small force on the small piston lifts a large load on the large piston.

   Hint: Same pressure, larger area → larger force.

10. 10.In a hydraulic system, does force multiplication violate conservation of energy?

    No. The large piston moves a smaller distance so that work input equals work output: $F_1 d_1 = F_2 d_2$ (for an ideal, frictionless system). Force is multiplied, distance is reduced.

    Hint: Work in = work out; distance trades for force.

11. 11.State the principle of a hydrostatic paradox.

    Liquid pressure at the base depends only on the vertical depth of liquid, not on the shape or amount of liquid. Vessels of different shapes with the same liquid height have the same base pressure.

    Hint: Pressure depends on height, not shape.

12. 12.Why does pressure at the same horizontal level in a connected static fluid stay equal?

    Since $P = P_0 + \rho g h$ depends only on depth $h$ (and density), all points at the same depth in a continuous fluid at rest are at equal pressure. This is why liquid finds its own level.

    Hint: Same depth → same pressure.

13. 13.State Archimedes' principle.

    A body wholly or partly immersed in a fluid experiences an upward buoyant force equal to the weight of the fluid displaced: $F_B = \rho_{fluid}\, V_{disp}\, g$.

    Hint: Upthrust = weight of displaced fluid.

14. 14.What is buoyant force (upthrust) and where does it act?

    The net upward force a fluid exerts on a submerged body, arising because pressure increases with depth. It acts at the centre of buoyancy — the centroid of the displaced fluid volume.

    Hint: Bottom pressure > top pressure → net up force.

15. 15.State the law of floatation.

    A floating body displaces a weight of fluid equal to its own weight. For floating: weight of body $=$ buoyant force, i.e. $\rho_{body}V_{body}\,g = \rho_{fluid}V_{disp}\,g$.

    Hint: Weight = weight of displaced fluid.

16. 16.When does a body float, sink, or remain suspended in a fluid?

    Compare densities: if $\rho_{body} < \rho_{fluid}$ it floats; if $\rho_{body} > \rho_{fluid}$ it sinks; if $\rho_{body} = \rho_{fluid}$ it stays fully submerged in equilibrium.

    Hint: Compare body and fluid densities.

17. 17.What fraction of a floating body is submerged?

    The submerged fraction equals the ratio of densities: $\dfrac{V_{sub}}{V_{body}} = \dfrac{\rho_{body}}{\rho_{fluid}}$.

    Hint: Density ratio gives submerged fraction.

18. 18.Define relative density (specific gravity).

    Ratio of a substance's density to the density of water at $4^\circ\text{C}$: $\text{RD} = \dfrac{\rho_{substance}}{\rho_{water}}$. It is dimensionless.

    Hint: Density compared to water.

19. 19.What is the apparent weight of a body immersed in a fluid?

    Apparent weight $=$ true weight $-$ buoyant force $= W - \rho_{fluid}V g$. The body seems lighter by the weight of fluid displaced.

    Hint: Subtract upthrust from real weight.

20. 20.Distinguish streamline (laminar) flow from turbulent flow.

    In streamline flow every fluid particle passing a point follows the same smooth path with velocity below a critical value. In turbulent flow the motion is irregular, with eddies, above the critical speed.

    Hint: Orderly paths vs chaotic eddies.

21. 21.What is a streamline, and can two streamlines cross?

    A streamline is a path whose tangent at every point gives the fluid velocity direction there. Two streamlines never cross — otherwise the fluid would have two velocities at the crossing point.

    Hint: Tangent = velocity; no crossing.

22. 22.State the equation of continuity and the conservation law behind it.

    $A_1 v_1 = A_2 v_2$, i.e. $Av = \text{constant}$. It expresses conservation of mass for an incompressible fluid in steady flow.

    Hint: Area times speed is constant.

23. 23.According to continuity, where does a fluid flow faster in a pipe?

    Where the cross-sectional area is smaller. Since $Av$ is constant, a narrower section gives a higher speed (and vice versa).

    Hint: Narrow → fast, wide → slow.

24. 24.Define volume flow rate and its relation to continuity.

    Volume flow rate $Q = Av$ (volume crossing a section per unit time, in $\text{m}^3\text{s}^{-1}$). Continuity says $Q$ is the same at all cross-sections for incompressible steady flow.

    Hint: $Q = Av$ stays constant.

25. 25.State Bernoulli's theorem.

    For steady, incompressible, non-viscous flow: $P + \tfrac{1}{2}\rho v^2 + \rho g h = \text{constant}$ along a streamline. It is the energy-conservation law per unit volume.

    Hint: Pressure + KE + PE per volume = constant.

26. 26.List the assumptions underlying Bernoulli's equation.

    The fluid is (1) incompressible, (2) non-viscous (no friction), (3) in steady (streamline) flow, and (4) irrotational. Energy is conserved along a streamline.

    Hint: Ideal fluid, steady flow.

27. 27.Identify each term of Bernoulli's equation as a form of energy.

    $P$ = pressure energy per unit volume; $\tfrac{1}{2}\rho v^2$ = kinetic energy per unit volume; $\rho g h$ = potential energy per unit volume. Their sum is constant.

    Hint: Pressure, kinetic, potential — all per unit volume.

28. 28.For a horizontal pipe, how does Bernoulli's theorem relate pressure and speed?

    With $h$ constant, $P + \tfrac{1}{2}\rho v^2 = \text{constant}$, so where speed is higher the pressure is lower. Fast flow → low pressure.

    Hint: Faster flow means lower pressure.

29. 29.State Torricelli's law for efflux speed from a small orifice.

    $v = \sqrt{2gh}$, where $h$ is the depth of the orifice below the free liquid surface. The efflux speed equals that of free fall through height $h$.

    Hint: Same as free-fall speed $\sqrt{2gh}$.

30. 30.How does an aeroplane wing (aerofoil) generate lift?

    Its shape makes air move faster over the top than the bottom. By Bernoulli, higher speed above → lower pressure above, so the net upward pressure difference provides lift.

    Hint: Faster air on top → lower pressure → lift.

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