Bernoulli's Theorem + Continuity
Properties of Matter
35
JEE Qs
10%
Hard
75
min
Thoroughly understand the assumptions and the physical meaning of each term in Bernoulli's equation to apply it correctly in diverse problem scenarios.
🧮 Key Formulas
✅ Key Points for JEE
- 1The Equation of Continuity (A₁v₁ = A₂v₂) is a statement of mass conservation for an incompressible fluid in steady flow.
- 2Bernoulli's Theorem (P + ½ρv² + ρgh = constant) is a statement of energy conservation for an ideal fluid (incompressible, non-viscous) in steady, streamline flow.
- 3In horizontal flow, an increase in fluid speed is associated with a decrease in pressure, and vice-versa (dynamic pressure effect).
- 4Always identify two suitable points along a streamline for applying Bernoulli's equation and carefully establish a consistent reference level for the potential energy term (h).
⚠️ Common Mistakes
- ✕Applying Bernoulli's Theorem without considering its underlying assumptions (ideal fluid, steady flow, incompressible, streamline flow).
- ✕Confusing absolute pressure with gauge pressure or not correctly accounting for atmospheric pressure at free surfaces.
- ✕Incorrectly identifying velocities or pressures at the chosen points, especially assuming zero velocity at a large tank's surface when it's emptying.
📝 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