Flow Past Through Submerged Body

Course: Fluid Mechanics — Practice MCQs, solutions, formulas & past entrance questions.

Chapter:

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1. Distinguish between pressure and friction drag. Explain with sketches, why airfoil is designed as a streamlined body. [2074-Ashwin ][5]

2. A kite has an effective area of `0.6 m^2` and mass 0.4 kg. It experience a drag of 15 N in a wind speed of 40 km/hr. Determine
  • tension in chord if it makes an angle of `45^0` with horizontal.
  • lift coefficient for kite
Consider density of air as 1.2 kg/`m^3`. [2070-Ashad ][8]

3. Streamlined Body

Streamlined Body:

A streamlined body is a body having a shape that lowers the friction drag between a fluid, like air and water, and an object moving through that fluid. In other words, A streamlined body is defined as that body whose surface is aligned with the streamlines, when the body is placed in the flow.

 Streamlined body experiences drag mainly due to Viscous/Frictional drag, which depends on the surface area exposed to fluid. Since the drag on the streamlined body is low, the lift/drag ratio is high.In this case, the separation usually takes place at the trailing edge.

An example of streamlined body is a thin aerofoil.


Bluff Body:

 A bluff body is defined as that body whose surface is not aligned with the stream-lines, when placed in the flow. Thus, the body offers less resistance in terms of Viscous/Frictional drag. There is a very large pressure drag, due to eddy formation after the body leading to a large wake region. Thus the pressure drag depends on the cross sectional area of the body rather than the surface area exposed.


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4. An aircraft weighing 1000 KN when empty has a wing area of 220 `m^2`. It is to take off at a velocity of 300km/hr and a `20^0` angle of attack. Determine allowable weight of cargo and power required for engine. Take density of air as 1.2 kg/`m^3`. Assume coefficient of lift for wing at `20^0` angle of attack as 1.42 and coefficient of drag as 0.17. [2073-Shrawan ][5]

5. A 2mm diameter spherical ball of unit weight 117.5 KN/`m^3` is dropped in a mass of fluid of viscosity 15 poise and specific gravity 0.95. Find out drag force, skin drag and terminal velocity of ball. [2068-Chaitra ][8]

6. Explain drag of a Cylinder.

Consider a real fluid flowing past a cylinder of length L and diameter D. the drag coefficient is,

`F_D=C_D*(rho*U^2)/2*A`

Where A is the projected area, which is equal to `LD` for a cylinder.

At very small velocities, `R_e<0.5` the fluid sticks to the cylinder all the way round and never separates from the cylinder. This produces a streamline pattern similar to that of an ideal fluid as shown in figure. The dynamic pressure is achieved at the front stagnation point and vacuum equal to the dynamic pressure exists at the top and bottom where the velocity is at its greatest. 

As the velocity increases, the boundary layer breaks away and eddies are formed behind as shown in figure. The drag pressure increases at the front due to the pressure behind and drag pressure drops at the back. 

A further increase in velocity cause eddies to elongate and the drag coefficient becomes nearly constant as shown in figure. The pressure distribution shows that ambient pressure exists at the rear of the cylinder.

At Reynolds number of around 90, the vortices break away alternatively from the top and bottom of the cylinder producing a vortex street in the wake as shown in figure. The pressure distribution shows the vacuum at the rear.

Drag Coefficient as a function of Reynolds Number:

  • For `R_e<1`the flow pattern will be symmetrical.

  • For `R_e =1 1 to 2000, `C_D` decreases and attains a minimum value of 0.95 at `R_e`=2000.

  • For `R_e=2000` to `3*10^4`, `C_D` increases and become 1.2 at `R_e=3*10^4`

  • For `R_e=3*10^4` to `3*10^5`, `C_D` decreases and its value becomes 0.3 at a value of `R_e=3*10^5`

  • For `R_e=3*10^6`, `C_D` increases and attains a value of o.7 in the end.

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7. Define aerofoil with accepted terminology with neat sketch. A wing with a span of 22m and 64 `m^2` plan area moves horizontally with a velocity of 760 kmhp. If wing supports 280 KN, find:
  • Required value of lift coefficient.
  • Induced drag.
Take density of air as 0.526kg/`m^3`. [2072-Kartik ][8]

8. A jet plane having a wing area of `30 m^2` and weighing 28 KN flies at 900 km/hr. The engine develops 8000 KW and has a mechanical efficiency of 70%. Determine lift and drag coefficient for wind taking density of air as 1.2 kg/`m^3`. [2069-Chaitra ][4]

9. Water flows over 0.3 m long nad 0.1 m wide flat plate at 15 m/s parallel to it. Calculate
  • drag force on that portion of plate over which boundary layer is laminar.
  • total drag force on both sides of plate.
Take `rho=998` kg/`m^3` and `mu= 10^(-6)` `m^2`/s. [2074-Chaitra ][8]

10. Define aerofoil with accepted terminology with neat sketch. A kite which may be assumed to be a flat plate and mass 1 kg soars at an angle to horizontal. The tension in string holding kite is 60N when wind velocity is 50 km/hr horizontally and angle of string to horizontal direction is `35^0`. The density of air is 1.2 kg/`m^3`. Calculate drag coefficient for kite in given position if lift coefficient in same position is 0.45. Both coefficients have been used in full area of kite. [ 2068-Shrawan ][8]

Topics

This Chapter flow-past-through-submerged-body consists of the following topics

Flow Past Through Submerged Body

ioe fluid mechanics

Flow Past Through Submerged Body ioe solution

fluid mechanics solution

ioe question bank

Distinguish between pressure and friction drag. Explain with sketches, why airfoil is designed as a streamlined body.

;

A kite has an effective area of `0.6 m^2` and mass 0.4 kg. It experience a drag of 15 N in a wind speed of 40 km/hr. Determine
  • tension in chord if it makes an angle of `45^0` with horizontal.
  • lift coefficient for kite
Consider density of air as 1.2 kg/`m^3`.

;

Streamlined Body

;

An aircraft weighing 1000 KN when empty has a wing area of 220 `m^2`. It is to take off at a velocity of 300km/hr and a `20^0` angle of attack. Determine allowable weight of cargo and power required for engine. Take density of air as 1.2 kg/`m^3`. Assume coefficient of lift for wing at `20^0` angle of attack as 1.42 and coefficient of drag as 0.17.

;

A 2mm diameter spherical ball of unit weight 117.5 KN/`m^3` is dropped in a mass of fluid of viscosity 15 poise and specific gravity 0.95. Find out drag force, skin drag and terminal velocity of ball.

;

Explain drag of a Cylinder.

;

Define aerofoil with accepted terminology with neat sketch. A wing with a span of 22m and 64 `m^2` plan area moves horizontally with a velocity of 760 kmhp. If wing supports 280 KN, find:
  • Required value of lift coefficient.
  • Induced drag.
Take density of air as 0.526kg/`m^3`.

;

A jet plane having a wing area of `30 m^2` and weighing 28 KN flies at 900 km/hr. The engine develops 8000 KW and has a mechanical efficiency of 70%. Determine lift and drag coefficient for wind taking density of air as 1.2 kg/`m^3`.

;

Water flows over 0.3 m long nad 0.1 m wide flat plate at 15 m/s parallel to it. Calculate
  • drag force on that portion of plate over which boundary layer is laminar.
  • total drag force on both sides of plate.
Take `rho=998` kg/`m^3` and `mu= 10^(-6)` `m^2`/s.

;

Define aerofoil with accepted terminology with neat sketch. A kite which may be assumed to be a flat plate and mass 1 kg soars at an angle to horizontal. The tension in string holding kite is 60N when wind velocity is 50 km/hr horizontally and angle of string to horizontal direction is `35^0`. The density of air is 1.2 kg/`m^3`. Calculate drag coefficient for kite in given position if lift coefficient in same position is 0.45. Both coefficients have been used in full area of kite.

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