Drag on a Sphere

Q. For the laminar flow of water over a sphere, the drag coefficient $C_F$ is defined as $C_F=F/\left(\rho U^2{D}^2\right)$, where F is the drag force, $\rho$ is the fluid density, U is the fluid velocity and D is the diameter of the sphere. The density of water is 1000 kg/$m^3$. When the diameter of the sphere is 100 mm and the fluid velocity is 2 m/s, the drag coefficient is 0.5. If water now flows over another sphere of diameter 200 mm under dynamically similar conditions, the drag force (in N) on this sphere is_______

1. 20

Q.

In an experiment to verify Stokes law, a small spherical ball of radius r and density $\sigma$ falls under gravity through a distance h in the air before entering a tank of water. If the terminal velocity of the ball inside water is the same as its velocity just before entering the water surface, then the value of h is proportional to (ignore viscosity of air)

1. ${\mathrm{r}}^4$

2. $\mathrm{r}$

3. ${\mathrm{r}}^3$

4. ${\mathrm{r}}^2$

Q. The terminal velocity of a sphere settling in a viscous fluid varies as

1. The Reynolds number
2. The square of its diameter
3. Directly proportional to the viscosity of fluid
4. Its diameter

Q. When an ideal fluid flows past a sphere_____

1. Highest intensity of pressure occurs around the circumference at right angles to direction of flow
2. Lowest pressure intensity occurs at front stagnation point
3. Lowest pressure intensity occurs at rear stagnation point
4. Total drag is zero

Q. An aircraft is flying in level flight at a speed of 200 km/hr through air (density, $\rho =1.2kg/m^3$, and viscosity $\mu =1.6\times {10}^{-5}Ns/m^2$). The lift coefficient at this speed is 0.4 and the drag coefficient is 0.0065. The mass of the aircraft is 800 kg. The effective lift area of the aircraft is

1. $21.2m^2$
2. $10.6m^2$
3. $2.2m^2$
4. $1.1m^2$

Q. The terminal velocity of a small sphere settling in a viscous fluid varies as the

1. Inverse square of the diameter
2. Inverse of the diameter
   
3. First power of its diameter
4. Inverse of the fluid viscosity

Q. In the Stoke's experiment of falling sphere. if is found that a sphere of 5 mm diameter falls in a liquid with terminal velocity 20 mm/s giving a drag coefficient of 240. The ratio of specific gravities is 2.85. Which one of the following is the kinematic viscosity of the liquid in stokes?

1. 3.5
2. 10.0
3. 225.0
4. 1000.0

Q. If Stokes' law is considered valid below a Reynolds number of unity, then the largest raindrop that will fall in accordance with this law will have a diameter of approximately
$(assuming{\rho }_w=1000kg/m^3,{\rho }_a=1.3kg/m^3,v_w={10}^{-6}{m}^2/s,v_a=1.5\times {10}^{-5}{m}^2/s$

1. 0.75 mm
2. 0.3mm
3. 0.15
4. 0.075mm

Q. A solid sphere (diameter 6 mm) is rising through oil (mass density $900kg/m^3$, dynamic viscosity $0.7kg/m-s$) at a constant velocity of 1 cm/s. What is the specific weight of the material from which the sphere is made? (Take $g=9.81m/s^2$)

1. $4.3kN/m^3$
2. $5.3kN/m^3$
3. $8.7kN/m^3$
4. $12.3kN/m^3$

Q. An automobile with projected area $2.6m^2$ is running on a road with a speed of 120 km per hour. The mass density and the kinematic viscosity of air are $1.2kg/m^3$ and $1.5\times {10}^{-5}{m}^2/s$, respectively. The drag coefficient is 0.30.
The drag force on the automobile is

1. 620 N
2. 600 N
3. 580 N
4. 520 N

Q.

An automobile with projected area $2.6m^2$ is running on a road with a speed of 120 km per hour. The mass density and the kinematic viscosity of air are $1.2kg/m^3$ and $1.5\times {10}^{-5}{m}^2/s$, respectively. The drag coefficient is 0.30.
The metric horse power required to overcome the drag force is

1. 33.23
2. 31.23
3. 23.23
4. 20.23

Q. A sphere of certain diameter, when towed submerged under water, experiences a drag force of 4 N at a velocity of 1.5 m/s. If another sphere of twice the diameter of the sphere referred to above, is towed with the same velocity in water, the drag force experienced by this sphere will be

1. 8N
2. 16N
3. 24N
4. 32N

Q. A very small spherical particle of sand settles in a column of viscous liquid . If the Reynolds number corresponding to its terminal velocity is 0.25, the drag coefficient of the sand particle is :

1. 256
2. 128
3. 96
4. 64

Q. The aerodynamic drag on a sports car depends on its shape. The car has a drag coefficient of 0.1 with the windows and the roof closed. With the windows and the roof open, the drag coefficient becomes 0.8. The car travels at 44 km/h with the windows and roof closed for the same amount of power needed to overcome the aerodynamic drag, the speed of the car with the windows and roof open (round off to two decimal places), is ______km/h. (density of air and the frontal area may be assumed to be constant).

1. 22

Q.

The sphere of diameter 0.02 m falls in a fluid of kinematic viscosity of 10 stokes with a terminal velocity of 0.02 m/s. What is the value of the coefficient of drag on the falling sphere?

1. 40
2. 60
3. 80
4. 100

Q. Body M has twice the weight, twice the projected area and twice the drag coefficient of body N. How many times is the terminal velocity of the body M in air, compared to that of the body N ?

1. 8
2. 2
3. $\sqrt{2}$
4. $1/\sqrt{2}$

Q. When small sphere falls freely in stokes range through a water column, which of the following statement are correct?
1. Viscosity, surface tension and gravitational forces act on the sphere.
2. There is no turbulence possible in the wake of the falling sphere.
3. Drag coefficient, $C_d=R/24$, where R is Reynolds number.
4.Proximity of the boundary moderates the drag and lift coefficients.

1. 1 and 2
2. 2 and 3
3. 3 and 4
4. 2 and 4

Q. A man, 65 kg, descends to the ground with the helps of a parachute, 18 kg. The parachute is hemispherical in shape, 2 m diameter. Density of air can be taken as $0.00125g/c{m}^3$ and its kinematic viscosity as 0.15 stoke. What is the terminal velocity of the parachute? [Take $C_D,=1.5andg=1000cm/se{c}^2]$

1. 16.6 m/sec
2. 15.8 m/sec
3. 15.0m/sec
4. 14.1 m/sec

Q. A small spherical ball (ping-pong ball) of weight 250 milli Newton and diameter 40 mm is subjected to a constant vertical velocity of 25 m/s of air density $1.2kg/m^3$. What is the drag coefficient?

1. 0.42
2. 0.85
3. 1.0
4. 0.53