Bernoulli's Principle

As stated in NCERT Class 11, Chapter 10 (Mechanical Properties of Fluids), Bernoulli's principle expresses conservation of energy for streamline flow: $P+\frac{1}{2}\rho v^2+\rho gh=\text{constant}$. For a horizontal pipe the height term is constant, so the sum of pressure energy and kinetic energy per unit volume is fixed. The equation of continuity, $A_1{v}_1=A_2{v}_2$, tells us that where the pipe narrows the cross-sectional area drops and the speed rises. From Bernoulli's relation, if $v$ increases then $P$ must decrease to keep the total constant. Hence the pressure in the narrow section falls. The option claiming pressure increases with speed contradicts Bernoulli's relation. The option of unchanged pressure ignores the speed change. The option pairing lower pressure with lower speed has the speed dependence backwards, since continuity guarantees that the speed actually rises in the constriction. It is worth noting that this is purely an energy trade-off: the fluid does not gain or lose total energy, it merely converts pressure energy into kinetic energy as it accelerates. A consistency check confirms the well-known result that fast-moving fluid exerts lower pressure, which underlies the working of carburettors, atomisers, and the lift generated over an aircraft wing, so the pressure must indeed drop where the pipe narrows.