This set of Advanced Mechanical Operations Questions and Answers focuses on “Drag Force on Spherical Particle”.

1. Which of the following is the correct form of Stoke’s law?

(Here, C_{D} represents Drag coefficient and N_{Re} represents Reynolds number)

a) C_{D} = 24 / N_{Re}

b) C_{D} = 24 * N_{Re}

c) C_{D} = 18 / N_{Re}

d) C_{D} = 18 * N_{Re}

View Answer

Explanation: Stoke’s law is the expression for C

_{D}when the Reynolds number is less than 0.2. According to Stoke’s law, C

_{D}= 24/N

_{Re}and, it explains the relationship between the drag coefficient with density of the sphere, velocity of flow, diameter of the sphere and viscosity of the fluid.

2. What is the value of C_{D} corresponding to a Reynold’s number between 5 and 1000?

a) 0.3

b) 0.4

c) 0.2

d) 0.1

View Answer

Explanation: C

_{D}refers to the drag coefficient, a dimensionless quantity that represents the resistance of an object in a fluid environment such air or water. The value of C

_{D}corresponding to a Reynold’s number between 5 and 1000 is 0.4. This is also a very helpful tip that can be used in problems.

3. Under which condition, is the Cunningham correction factor applicable for very small particles?

a) When particle size is far greater than the gas mean free path

b) When particle size is far lesser than the gas mean free path

c) When particle size becomes comparable to the gas mean free path

d) Cunningham factor is applicable for small particles under all conditions

View Answer

Explanation: Slip occurs when particles have a comparable size with that of the gas mean free path and this is when the Cunningham factor is used. The total drag force, when divided by the Cunningham correction factor, gives an expression that accounts for the slip.

4. Under which circumstances is the Oseen formula valid for drag coefficient?

a) When the Reynolds number is between 0.3 and 5

b) When the Reynolds number is between 0.2 and 4

c) When the Reynolds number is between 0.3 and 4

d) When the Reynolds number is between 0.2 and 5

View Answer

Explanation: Oseen was a Swedish scientist who accounted for the increase of inertial forces when Reynolds number is between 0.2 and 5. He gave the expression for C

_{D}as

C

_{D}= 24/N

_{Re}times [1 + (3 / (16 * N

_{Re}))]

5. The total drag is a sum of the skin drag and the pressure drag. Which among of the following options, states the correct formula for skin drag and pressure drag?

(Here µ stands for dynamic viscosity of fluid, D stands for diameter of the sphere and U stands for velocity of flow of fluid.)

a) 2πµDU, 2πµDU

b) 1πµDU, 2πµDU

c) 2πµDU, πµDU

d) 3πµDU, πµDU

View Answer

Explanation: Total drag is accounted by two thirds of the skin drag and one third of the pressure drag. Skin drag, also called friction drag, is due to the friction offered by the fluid, while pressure drag is due to the pressure difference between the sides of the sphere.

6. What are the dimensions of drag coefficient?

a) Dimensionless

b) MLT^{-2}

c) ML^{-3}

d) L

View Answer

Explanation: Drag coefficient is a dimensionless quantity that gives a measure of the drag experienced by the body while flowing in a fluid. Drag force is directly proportional to drag coefficient. Therefore, greater the drag coefficient, greater the drag force.

7. Let F_{G} be the gravitational force, F_{D} be the drag force and F_{B} be the buoyant force. Which of the following best describes the relation between these forces when a sphere falls into a fluid with terminal velocity?

a) F_{G} + F_{D} = F_{B}

b) F_{G} + 2F_{B} = F_{D}

c) 2F_{B} + F_{D} = F_{G}

d) F_{B} + F_{D} = F_{G}

View Answer

Explanation: The sum of the buoyant force and the drag force gives gravitational force. Buoyant force is an upward force exerted by the fluid, resisting the downward motion of body. Gravitational force is the force due to the effect of gravity. Drag force acts opposite to the direction of the moving body.

8. Calculate the drag force on a ball of diameter of 80mm, flowing through air. The density of air is 1.25 kg/m^{3} and the ball flows with a velocity of 7m/s. The Reynolds number is 3730.

a) 0.077 N

b) 76969 N

c) 0.011 N

d) 10995 N

View Answer

Explanation: Since, the Reynold number is between 1000 and 10,000 the drag coefficient C

_{D}= 0.5.

Drag force F

_{D}= C

_{D}* A * Ro * U

^{2}/2.

Here A is the projected Area

A = π * D

^{2}/4.

On substituting the values of C

_{D}, A and Ro (=1.25 kg/m

^{3}) and U (=7m/s)

F

_{D}= 0.5 * π * .08

^{2}/4 * 1.25 * 7

^{2}/2

F

_{D}= .077 N

9. Which component of the total force is perpendicular to the direction of motion? What are the dimensions of this component?

a) Lift, MLT^{-1}

b) Drag MLT

c) Drag, MLT^{-2}

d) Lift, MLT^{-2}

View Answer

Explanation: Since lift is a component perpendicular to the direction of motion, it has the dimensions same as that of force, MLT

^{-2}. Lift is caused because of a difference in the air pressures. Drag on the other hand, is due to the difference in air pressures, as well as, friction.

10. Select the incorrect statement.

a) Drag depends inversely on mass

b) Drag is independent of shape

c) Drag linearly depends on velocity

d) Drag depends on compressibility

View Answer

Explanation: Drag depends directly on the mass of the object. Several factors such as shape of the body, viscosity of fluid and lift experienced velocity of flow influence drag force. Drag is proportional to velocity in case of laminar flow however, it is proportional to the square of velocity in case of turbulent flow.

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