MPSC 2024 Prelims Paper-I · Question 52 of 100

Correct — option (4), None of the above. This is a negative stem: the word 'not' is printed in bold in the paper, so the question asks which of the listed items is NOT an application of Bernoulli's equation. The answer is that none of them fails the test, because all three are textbook applications of it. Bernoulli's equation states that for the steady, incompressible, non-viscous flow of a fluid along a streamline the sum of the pressure, the kinetic energy per unit volume and the potential energy per unit volume stays constant — pressure plus half rho v squared plus rho g h does not change. Its most useful consequence is that where a fluid speeds up, its pressure falls. The Venturi arrangement — the paper prints 'Ventury', after Giovanni Battista Venturi — is built directly on that consequence: a pipe is narrowed, the fluid must move faster through the constriction to carry the same volume per second, and the pressure there drops, which is used both to measure the rate of flow and, in the pump version, to suck a second fluid in through a side tube. An aspirator or filter pump is the same device under another name, a jet of water driven through a constriction whose low pressure draws air or gas out of a vessel; the atomiser, the sprayer, the Bunsen burner and the carburettor all belong to the same family. The speed of efflux is Bernoulli's equation applied to a tank with a hole in it: equate the pressure and height terms at the free surface and at the hole and the emerging speed comes out as the square root of twice g h, which is Torricelli's law. Three applications, no exception among them, so the escape option is the one that answers the question.

• (1)Aspirator pump — An aspirator pump, also called a filter pump, is a straightforward application of Bernoulli's principle rather than an exception to it. Water is forced through a narrow throat, its speed rises and its pressure consequently falls below atmospheric, and a side tube connected to the vessel being evacuated allows air to be drawn into the fast-moving stream and carried away. Because it depends on nothing but a pressure difference generated by the flow itself, it has no moving parts. Selecting it as the odd one out means the negation in the stem has not been read, or the device has been mistaken for a mechanical pump of the piston or vane type.
• (2)Ventury pump — The Venturi arrangement is perhaps the single most cited application of Bernoulli's equation, so it cannot be the item that fails to apply it. Narrowing a pipe forces the fluid through a smaller area, the equation of continuity requires the speed to rise in inverse proportion to that area, and Bernoulli's relation then requires the pressure to fall. The Venturi meter reads the rate of flow from the resulting pressure difference between the wide and narrow sections; the same geometry appears in the carburettor of a petrol engine and in the spray gun. The unfamiliar printed spelling should not disguise the device.
• (3)Speed of Efflux — Speed of efflux is the standard derivation performed with Bernoulli's equation in every introductory fluids chapter, not an exception to it. Apply the equation between the free surface of a liquid in a large open tank and a small hole a depth h below it: both points are at atmospheric pressure, the surface is descending so slowly that its kinetic term can be neglected, and the height difference converts entirely into kinetic energy at the hole, giving an efflux speed equal to the square root of twice g h. That result is Torricelli's law, and it is a consequence of Bernoulli's equation rather than an independent principle.

Bernoulli's equation is conservation of energy written for a flowing fluid. Along a streamline in steady, incompressible, non-viscous flow, the pressure energy, kinetic energy and potential energy per unit volume add to a constant, so any increase in one must be paid for by a decrease in the others. Paired with the equation of continuity, which says that the product of cross-sectional area and speed is constant along a tube of flow, it yields the result that underlies almost every application: constrict a pipe and the fluid accelerates, and where it accelerates the pressure drops. From that single idea come the Venturi meter and the Venturi pump, the aspirator or filter pump, the atomiser and spray gun, the carburettor, the Bunsen burner's air intake, the lift on an aerofoil and the swerve of a spinning ball, and the speed of efflux from an orifice. The assumptions matter as much as the result — real fluids are viscous, real flows can be turbulent, and gases are compressible at high speed — so the equation is an idealisation that works well for the moderate flows of ordinary laboratory and engineering situations and less well elsewhere.

MPSC's general science section leans on the standard applications listed in school physics chapters, and this question is answerable by anyone who can recall that list. Its real difficulty is procedural rather than conceptual: the negation in the stem is carried by a single bolded word, and a candidate reading quickly will answer the positive question instead — which of these IS an application — and then find three defensible choices and pick one at random. The discipline is to mark the negation before reading the options and to convert the task explicitly into a hunt for the exception. Where the exception does not exist, an escape option such as 'none of the above' becomes the answer, and this paper offers such escapes sparingly enough that their appearance is worth noticing.

• Bernoulli's equation states that for steady, incompressible, non-viscous flow along a streamline the sum of pressure, kinetic energy per unit volume and potential energy per unit volume remains constant.
• Combined with the equation of continuity it implies that a fluid speeds up where a pipe narrows and that its pressure falls there, which is the basis of the Venturi meter, the Venturi pump and the aspirator or filter pump.
• The speed of efflux from a small hole a depth h below the free surface of a liquid is the square root of twice g h, a result known as Torricelli's law and derived directly from Bernoulli's equation.
• Other standard applications include the atomiser and spray gun, the carburettor, the Bunsen burner, the dynamic lift on an aerofoil and the Magnus effect on a spinning ball.
• The equation assumes ideal flow — steady, incompressible, non-viscous and along a streamline — so it describes real fluids only approximately, and less well as viscosity, turbulence or compressibility become significant.

• Missing the negation in the stem and answering the positive question instead, which on this item leaves three defensible-looking choices
• Failing to recognise a device through an unfamiliar printed spelling, such as the Venturi arrangement appearing in another transliteration
• Treating Torricelli's law as an independent principle rather than as a direct consequence of Bernoulli's equation
• Dismissing an escape option such as 'none of the above' on principle, when a negative stem can legitimately have no exception among the items listed

Fluid mechanics appears in MPSC general science as application-matching — name a device and ask which principle it uses, or name the principle and ask which device does not use it — and Bernoulli's equation is the most frequently used principle in that family because so many everyday devices depend on it. The Commission favours negative stems in this section, so the same content can be set either way. It is worth memorising the standard application list as a block, since a question in either direction is then answered from the same recall, and worth noting that the negation is often carried by a single emphasised word that is easy to skim past.

No directly related past PYQ was found.

• practice — not a real PYQ

  The speed with which a liquid emerges from a small hole at a depth h below the free surface of a large open tank is given by which of the following expressions ?

  • (a)The square root of g h
  • (b)The square root of twice g h
  • (c)Twice g h
  • (d)g h divided by two

  Answer(b) The square root of twice g h — applying Bernoulli's equation between the free surface and the hole, both of which are at atmospheric pressure, converts the height difference entirely into kinetic energy at the orifice. The result is Torricelli's law, and it is the same speed a body would acquire by falling freely through the height h.

• practice — not a real PYQ

  Which of the following is the principle that explains why the pressure of a fluid falls where the pipe carrying it becomes narrower ?

  • (a)Pascal's law
  • (b)Archimedes' principle
  • (c)Bernoulli's principle together with the equation of continuity
  • (d)Stokes' law

  Answer(c) Bernoulli's principle together with the equation of continuity — continuity requires the fluid to speed up where the cross-section shrinks, and Bernoulli's relation then requires the pressure to fall to pay for the extra kinetic energy. Pascal's law concerns the transmission of pressure in a fluid at rest, Archimedes' principle concerns buoyancy, and Stokes' law concerns the viscous drag on a sphere.