Fluids- External Flow and Drag

Question 1

What is drag?

Answer 1

The force a flowing fluid exerts on a body in the flow direction

Question 2

What is friction drag?

Answer 2

Drag force depending on wall shear. Depends on surface area parallel to flow.

Question 3

What is pressure drag?

Answer 3

Drag force acting that depends on the pressure difference between the front and back faces of an object. The area of low pressure sucks the object back into it. Depends on projected frontal area.

Question 4

What is velocity boundary layer?

Answer 4

The region of flow above the plate bounded by δ in which the effects of the viscous shearing forces caused by fluid viscosity are felt

Question 5

How is δ defined?

Answer 5

The distance at the surface at which u=0.99V

Question 6

Difference between boundary layer region and irrotational flow region

Answer 6

In boundary, viscous effects and velocity changes significant. In irrotational, frictional effects negligible and velocity essentially constant.

Question 7

Formula for displacement thickness

Answer 7

δ*=S(1-u/U)dy

From 0 to δ

Question 8

Formula for momentum thickness

Answer 8

Θ=S(u/U)(1-u/U)dy

From 0 to δ

Question 9

Boundary layer equation

Answer 9

τw/ρU^2=dΘ/dx

Question 10

Formula for wall shear stress for laminar flow over plate

Answer 10

τw=2μU/δ

Question 11

Formula for δ over x (laminar)

Answer 11

δ/x=5.5/Re^1/2

Question 12

Formula for skin friction coefficient Cf

Answer 12

Cf=0.73/Re^1/2

Question 13

How is total drag force defined for laminar flow over flat plate?

Answer 13

D is integral of wall shear stress with respect to x times width of plate

Question 14

Formula for friction coefficient for laminar flow over plate

Answer 14

CD=1.328/Re^1/2

=D/(0.5ρU^2bL)

Question 15

Formulae for δ Cf and CD for turbulent flow over smooth plate

Answer 15

See page 10

Question 16

How to use analog of Moody chart for pipe flows for external flow

Answer 16

Find L/ε (length of plate over roughness) to know which line to use. Go up from Reynolds number to that line and find Cf. Or use formula if fully rough on page 10.

Question 17

Formula for CD for friction and pressure drag

Answer 17

CD=FD/(0.5ρV^2A)
A is parallel area for friction
A is frontal area for pressure

Question 18

How do different types of drag forces and coefficients combine

Answer 18

Added linearly

Question 19

When does a body in free fall reach terminal velocity?

Answer 19

When drag force equals weight minus buoyant force.

Question 20

Describe flow separation

Answer 20

At sufficiently high velocities, the fluid stream detached itself from the surface of the body when the surface changes level. Location of separation point depends on Re, ε and level of fluctuations in the free stream.

Question 21

Separated region

Answer 21

Region between body and fluid stream when the fluid separates. It is low pressure region behind the body where recirculation and backflows occur

Question 22

How does size of separated region relate to pressure drag?

Answer 22

Larger separated region means larger pressure drag

Question 23

Wake

Answer 23

The region of flow trailing the body where the effects of the body on velocity are felt

Question 24

How does streamlining work?

Answer 24

Decreases pressure drag by delaying boundary layer separation and reducing pressure difference between front and back of the body. Height of body is D, length is L.

Question 25

How do friction and pressure drag vary with D/L?

Answer 25

Pressure drag increases with increasing D/L
Friction drag decreases with increasing D/L
There is value of D/L where total drag is at minimum

Question 26

Stokes law

Answer 26

FD=3πμVD

Applicable to dust particles in air and suspended solid particles in water

Question 27

How does superposition work?

Answer 27

Consider a complex body as a combination of simple bodies and add the individual drag coefficients to get approximate value.

Question 28

Why is there a dip in CD for flow over a smooth cylinder or sphere at high Re?

Answer 28

Due to flow separation point. The laminar boundary layer becomes turbulent so clings on to body longer before detaching so there is less pressure drag.

Question 29

What happens to CD for smooth sphere and cylinder as Re increases?

Answer 29

See top of page 19 for details.

Question 30

How does roughness impact CD for spheres and cylinders?

Answer 30

See bottom of page 19 for graph. Depends on Re