Bernoulli's Theorem — Applications, Venturimeter
Properties of Matter
14
JEE Qs
8%
Hard
75
min
Master the conditions for Bernoulli's Theorem and practice applying it with the Equation of Continuity to solve problems involving fluid flow through varying cross-sections and heights.
🧮 Key Formulas
✅ Key Points for JEE
- 1Bernoulli's Theorem is a statement of energy conservation for an ideal fluid (incompressible, non-viscous) in steady, irrotational flow along a streamline.
- 2It relates pressure (P), kinetic energy per unit volume ((1/2)ρv^2), and potential energy per unit volume (ρgh) at any two points along a streamline.
- 3An increase in fluid speed generally leads to a decrease in pressure (dynamic pressure effect) and vice-versa, assuming changes in height are negligible.
- 4Always apply Bernoulli's equation between two points on the SAME streamline and ensure the fluid meets the ideal fluid conditions.
- 5Key applications include the Venturimeter (for measuring flow rate), Torricelli's law for efflux velocity, and the qualitative explanation of lift on an airfoil.
⚠️ Common Mistakes
- ✕Not simultaneously applying the Equation of Continuity (A1v1 = A2v2) when dealing with changing cross-sectional areas, which is often required to relate velocities.
- ✕Incorrectly choosing the two points for applying Bernoulli's equation, especially if they are not on the same streamline or if the flow is not steady/irrotational.
- ✕Confusing gauge pressure with absolute pressure, or inconsistent use of a reference level for 'h' in the potential energy term (ρgh).
- ✕Forgetting the fundamental assumptions and conditions for Bernoulli's theorem to be valid (ideal fluid: incompressible, non-viscous, steady, irrotational flow).
📝 Practice Questions
See allQ47.Two soap bubbles of radius 2 cm and 4 cm , respectively, are in contact with each other. The radius of curvature of the common surface, in cm , is ______ . and
Q27.A small rigid spherical ball of mass M is dropped in a long vertical tube containing glycerine. The velocity of the ball becomes constant after some time. If the density of glycerine is half of the density of the ball, then the viscous force acting on the ball will be (consider g as acceleration due to gravity) (1) 2 Mg (2) Mg (3) 3 2 Mg (4) Mg2
Q41. A tube of length L is shown in the figure. The radius of cross section at the point (1) is 2 cm and at the point (2) is 1 cm , respectively. If the velocity of water entering at point (1) is 2 m/s, then velocity of water leaving the point (2) will be (1) 4 m/s (2) 2 m/s (3) 6 m/s (4) 8 m/s
Q30.A massless spring gets elongated by amount x1 under a tension of 5 N . Its elongation is x2 under the tension of 7 N . For the elongation of (5x1 −2x2), the tension in the spring will be, (1) 39 N (2) 15 N (3) 11 N (4) 20 N
Q32.Water flows in a horizontal pipe whose one end is closed with a valve. The reading of the pressure gauge attached to the pipe is P1 . The reading of the pressure gauge falls to P2 when the valve is opened. The speed of water flowing in the pipe is proportional to (1) P1 −P2 (2) (P1 −P2)4 (3) (P1 −P2)2 (4) √P1 −P2
Q48.An air bubble of radius 1.0 mm is observed at a depth of 20 cm below the free surface of a liquid having surface tension 0.095 J/m2 and density 103 kg/m3 . The difference between pressure inside the bubble and atmospheric pressure is _____ N/m2 . (Take g = 10 m/s2 )
NCERT Chapters
- Class 11 Physics Ch 10: Mechanical Properties of Fluids