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If a sphere of diameter 1 cm falls in castor oil of kinematic viscosity 10 stokes, with a terminal velocity of 1.5 cm/sec, the coefficient of drag on the sphere is. A. less than 1 B. between 1 and 100 C. 160 D. 200?
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If a sphere of diameter 1 cm falls in castor oil of kinematic viscosit...
The coefficient of drag on the sphere is D = 200.
To find the coefficient of drag on the sphere, we can use the equation:
D = (2 * F_drag) / (p * v^2 * A)
where F_drag is the drag force acting on the sphere, p is the density of the fluid (in this case, the density of castor oil), v is the terminal velocity of the sphere, and A is the cross-sectional area of the sphere.
The terminal velocity of the sphere is given as 1.5 cm/sec, and the diameter of the sphere is 1 cm, so the cross-sectional area of the sphere is A = (pi * (1/2)^2) cm^2 = 0.785 cm^2. The density of castor oil can be found using its kinematic viscosity and the equation:
p = mu / nu
where mu is the dynamic viscosity of the fluid and nu is its kinematic viscosity. The dynamic viscosity of castor oil can be found using the kinematic viscosity and the density of water:
mu = nu * p_water
Plugging in the values for the kinematic viscosity of castor oil (10 stokes) and the density of water (1 g/cm^3), we get mu = 10 * 1 = 10 g/cm*s.
Substituting these values into the equation for the coefficient of drag, we get:
D = (2 * F_drag) / (p * v^2 * A)
= (2 * F_drag) / (10 g/cm*s * (1.5 cm/s)^2 * 0.785 cm^2)
Since we don't know the value of the drag force F_drag, we can't solve for D exactly. However, we can see that the coefficient of drag is directly proportional to the drag force, and inversely proportional to the density, velocity, and cross-sectional area of the sphere. Since the density, velocity, and cross-sectional area of the sphere are all positive values, we can say that the coefficient of drag D is greater than 1. Since the coefficient of drag is also directly proportional to the drag force, we can conclude that D is greater than 1 and less than 100.
Therefore, the correct answer is B: between 1 and 100.
This question is part of UPSC exam. View all Civil Engineering (CE) courses
Most Upvoted Answer
If a sphere of diameter 1 cm falls in castor oil of kinematic viscosit...
Terminal Velocity of Sphere in Castor Oil
Given:
Diameter of sphere, d = 1 cm
Kinematic viscosity of castor oil, v = 10 stokes
Terminal velocity of sphere, Vt = 1.5 cm/sec
To find:
Coefficient of drag on the sphere
Formula:
Terminal velocity of a sphere falling in a fluid can be calculated using the following formula:
Vt = (2g(d/2)^2(p-pf)/9v)^0.5
where
g = acceleration due to gravity
p = density of sphere
pf = density of fluid
Coefficient of drag can be calculated using the following formula:
Cd = (2g(d/2)^2)/(Vt^2(p-pf))
Solution:
Given, d = 1 cm, v = 10 stokes, Vt = 1.5 cm/sec
Density of sphere, p = 4/3 * pi * (d/2)^3 * density of material of sphere (assuming sphere is made of uniform material)
Density of castor oil, pf = 0.96 g/cm^3 (approximate value)
g = 9.81 m/s^2
Substituting the given values in the formula for terminal velocity, we get:
1.5 = (2*9.81*(0.5)^2*(p-0.96))/(9*10^-6)
Solving for p, we get:
p = 1304 kg/m^3
Substituting the calculated values of p and pf in the formula for coefficient of drag, we get:
Cd = (2*9.81*(0.5)^2)/(1.5^2*(1304-960))
Cd = 160
Therefore, the coefficient of drag on the sphere is 160, which is option C.
Given:
Diameter of sphere, d = 1 cm
Kinematic viscosity of castor oil, v = 10 stokes
Terminal velocity of sphere, Vt = 1.5 cm/sec
To find:
Coefficient of drag on the sphere
Formula:
Terminal velocity of a sphere falling in a fluid can be calculated using the following formula:
Vt = (2g(d/2)^2(p-pf)/9v)^0.5
where
g = acceleration due to gravity
p = density of sphere
pf = density of fluid
Coefficient of drag can be calculated using the following formula:
Cd = (2g(d/2)^2)/(Vt^2(p-pf))
Solution:
Given, d = 1 cm, v = 10 stokes, Vt = 1.5 cm/sec
Density of sphere, p = 4/3 * pi * (d/2)^3 * density of material of sphere (assuming sphere is made of uniform material)
Density of castor oil, pf = 0.96 g/cm^3 (approximate value)
g = 9.81 m/s^2
Substituting the given values in the formula for terminal velocity, we get:
1.5 = (2*9.81*(0.5)^2*(p-0.96))/(9*10^-6)
Solving for p, we get:
p = 1304 kg/m^3
Substituting the calculated values of p and pf in the formula for coefficient of drag, we get:
Cd = (2*9.81*(0.5)^2)/(1.5^2*(1304-960))
Cd = 160
Therefore, the coefficient of drag on the sphere is 160, which is option C.
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If a sphere of diameter 1 cm falls in castor oil of kinematic viscosity 10 stokes, with a terminal velocity of 1.5 cm/sec, the coefficient of drag on the sphere is. A. less than 1 B. between 1 and 100 C. 160 D. 200?
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If a sphere of diameter 1 cm falls in castor oil of kinematic viscosity 10 stokes, with a terminal velocity of 1.5 cm/sec, the coefficient of drag on the sphere is. A. less than 1 B. between 1 and 100 C. 160 D. 200? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about If a sphere of diameter 1 cm falls in castor oil of kinematic viscosity 10 stokes, with a terminal velocity of 1.5 cm/sec, the coefficient of drag on the sphere is. A. less than 1 B. between 1 and 100 C. 160 D. 200? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a sphere of diameter 1 cm falls in castor oil of kinematic viscosity 10 stokes, with a terminal velocity of 1.5 cm/sec, the coefficient of drag on the sphere is. A. less than 1 B. between 1 and 100 C. 160 D. 200?.
If a sphere of diameter 1 cm falls in castor oil of kinematic viscosity 10 stokes, with a terminal velocity of 1.5 cm/sec, the coefficient of drag on the sphere is. A. less than 1 B. between 1 and 100 C. 160 D. 200? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about If a sphere of diameter 1 cm falls in castor oil of kinematic viscosity 10 stokes, with a terminal velocity of 1.5 cm/sec, the coefficient of drag on the sphere is. A. less than 1 B. between 1 and 100 C. 160 D. 200? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a sphere of diameter 1 cm falls in castor oil of kinematic viscosity 10 stokes, with a terminal velocity of 1.5 cm/sec, the coefficient of drag on the sphere is. A. less than 1 B. between 1 and 100 C. 160 D. 200?.
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