Streamline vs Turbulent Flow — Reynolds number
Properties of Matter
14
JEE Qs
8%
Hard
60
min
Master the Reynolds number formula, its physical interpretation, and the critical values for flow regime prediction, as problems often involve identifying flow type or calculating a required parameter for a specific flow regime.
🧮 Key Formulas
✅ Key Points for JEE
- 1Streamline (laminar) flow involves smooth, orderly fluid motion in layers without mixing, while turbulent flow is characterized by chaotic, irregular, and swirling fluid motion with significant mixing.
- 2Reynolds number (Re) is a dimensionless quantity that quantifies the ratio of inertial forces to viscous forces within a fluid and is used to predict the flow regime.
- 3A low Reynolds number indicates dominant viscous forces and generally results in laminar flow; a high Reynolds number indicates dominant inertial forces and leads to turbulent flow.
- 4The critical Reynolds number values (e.g., 2000 and 3000 for pipes) are empirical and serve as thresholds for transition between flow types. These values can vary with flow geometry.
- 5Turbulent flow causes significantly higher energy dissipation (pressure drop) compared to laminar flow due to the increased internal friction and mixing.
⚠️ Common Mistakes
- ✕Confusing the characteristic length 'd' (often pipe diameter) with radius or other dimensions, leading to incorrect Reynolds number calculation.
- ✕Not understanding the dimensionless nature of Reynolds number and attempting to assign units to it, or failing to use consistent units for other variables.
- ✕Incorrectly recalling or applying the critical Reynolds number ranges for specific flow geometries (e.g., assuming pipe values apply universally).
- ✕Failing to distinguish between average velocity (v) in the Reynolds number formula and instantaneous or local velocities in the fluid.
📝 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