A solid spherical bead of lead (uniform density = 11000 kg/m 3 ) of diameter d = 0.1 mm sinks with a constant velocity V in a large stagnant pool of a liquid (dynamic viscosity = 1.1 × 10 -3 kg∙m -1 ∙s -1 ). The coefficient of drag is given by C_{D} = \frac{24}{Re}, where the Reynolds number (Re) is defined on the basis of the diameter of the bead. The drag force acting on the bead is expressed as D = (C_{D})(0.5\rho V^{2}) (\frac{\pi d^{2}}{4}) , where ρ is the density of the liquid. Neglect the buoyancy force. Using g = 10 m/s 2 , the velocity V is __________ m/s.

GATE Mechanical Engineering (ME) 2022 Shift 1 Solved Paper

Question : 43 of 65

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A solid spherical bead of lead (uniform density = 11000 kg/m³) of diameter d = 0.1 mm sinks with a constant velocity V in a large stagnant pool of a liquid (dynamic viscosity = 1.1 × 10^-3 kg∙m^-1∙s^-1). The coefficient of drag is given by

C_{D} = \;{24}/{Re}

, where the Reynolds number (Re) is defined on the basis of the diameter of the bead. The drag force acting on the bead is expressed as

D = (C_{D})(0.5ρ V^{2}) (\;{π\;d^{2}}/{4}) ,

where ρ is the density of the liquid. Neglect the buoyancy force. Using g = 10 m/s², the velocity V is __________ m/s.

$\;{1}/{24}$
$\;{1}/{6}$
$\;{1}/{18}$
$\;{1}/{12}$

Validate

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