Which one of the following is not an application of Bernoulli equation ?

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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.

Why the other options are wrong — (a) 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.  (b) 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.  (c) 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.

Concept: 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.

State PCS 2024 Q52 — Science & Technology PYQ with Answer

State PCS 2024 Q52 — Science & Technology PYQ with Answer