Exams › JEE Main › Physics
The radius of a pipeline's cross-section decreases gradually as r = r0*e^(-alpha*x), where alpha = 0.50 m⁻¹ and x is the distance from the pipe inlet. For an incompressible fluid in steady flow, find the ratio of Reynolds numbers Re_final/Re_initial between two cross-sections separated by deltaₓ = 3.2 m.
- e^(-1.6)
- e^(1.6)
- e^(-3.2)
- e^(3.2)
Correct answer: e^(1.6)
Solution
Continuity gives v proportional to 1/r². Reynolds number Re = rho v (2r)/eta is proportional to v*r proportional to (1/r²)*r = 1/r. So Re_final/Re_initial = r_initial/r_final = e^(-alpha*x1)/e^(-alpha*x2) = e^(alpha(x2-x1)) = e^(alpha*deltaₓ) = e^(0.5*3.2) = e^(1.6).
Related JEE Main Physics questions
- A body is in motion inside a liquid, and the viscous resistive force on it is directly proportional to its speed. What are the dimensions of the proportionality constant?
- A capillary tube has its inner surface lined with wax and is then placed in water. Relative to a clean, unwaxed capillary, how do the contact angle (θ) and the height (h) to which water rises change?
- A charged, isolated spherical soap bubble of radius r has internal pressure equal to atmospheric pressure. If the charge on the bubble is given by Xπ√(2Tε), what is the value of X?
- Two capillary tubes, one of length L and radius R and the other of length 2L and radius 2R, are joined one after the other in series. If the flow rate through a single capillary is X = πPR⁴ / 8ηL, then the combined flow rate through the series arrangement is:
- A liquid will fail to wet the surface of a solid when the angle of contact is
- A gold sphere of a given size falls through a viscous liquid and attains a terminal speed of 0.2 m/s. If the gold has density 19.5 kg/m³ and the liquid has density 1.5 kg/m³, what terminal speed will a silver sphere of the same size have in the same liquid, given that silver has density 10.5 kg/m³?
⚔️ Practice JEE Main Physics free + battle 1v1 →