skin friction coefficient

Question 1

skin friction coefficient (Cf)

Answer 1

measures the resistance a fluid exerts on a surface

lamina (< 10^5):
= 1.33 / sqrt(Re)

transitional (10^5 - 3 x10^6):
= 0.074/Re^1/5 - 1700/Re

turbulent (> 3 x10^6):
= 0.074/Re^1/5

Question 2

what is the difference between Cd and Cf

Answer 2

Skin Friction Coefficient (Cf)
Drag Coefficient (Cd)

*Cf focuses only on frictional resistance (skin friction) at the surface of the object. Cd accounts for all types of drag (friction and pressure drag) acting on the object.
*Cf is a local coefficient for the surface, while Cd is a global coefficient for the entire object.

Cf is more specific to surface roughness and the interaction between the fluid and the surface.
Cd represents the overall drag on an object, considering both friction and pressure effects.

Question 3

boundary layer thickness δ(x) for a turbulent flow over a flat plate

Answer 3

= 0.38x / Re^1/5

distance from the leading edge of the surface, (x)
boundary layer thickness at position x, (δ(x))

Question 4

boundary layer thickness δ(x) for a lamina flow over a flat plate

Answer 4

= 0.52x / sqrt(Re)

distance from the leading edge of the surface, (x)
boundary layer thickness at position x, (δ(x))

Question 5

Reynolds number for external flow along a plate

Answer 5

Re = Ux / v

free-stream velocity, velocity of the fluid far from the surface (U)
distance from the leading edge of the plate (x)
kinematic viscosity of the fluid (v)

Question 6

drag force (Fd) on a flat plate

Answer 6

= Cf * 1/2ρU^2 * A

Cf is the skin friction coefficient
ρ is the fluid density,
U is the free-stream velocity,
A is the reference area (plate area exposed to the flow)

Question 7

when are viscous forces negligent

Answer 7

outside the boundary layer

Question 8

flow separation

Answer 8

when the boundary layer is slowed so much causing it to separate, caused by an adverse pressure gradient

Question 9

wake

Answer 9

are the eddies created from flow seperation, this rapid separation causes an area of low pressure

Question 10

pressure drag

Answer 10

also known as form drag, is the force produced by the low pressure of the wake acting to slow down the body

Question 11

Projected area

Answer 11

refers to the two-dimensional area of an object as seen from a specific viewpoint or direction.

Question 12

How does turbulent flow reduce pressure drag by delaying flow separation?

Answer 12

Turbulent flow increases the mixing of high-energy fluid from the outer layers with low-energy fluid near the surface. This boosts the momentum of the boundary layer, enabling it to overcome an adverse pressure gradient for longer. By delaying flow separation, the turbulent flow reduces the size of the wake behind the object, which decreases pressure drag.

Question 13

different types of flow around a sphere

Answer 13

stokes flow, smooth flow around the sphere:
Cd = 24/Re

allen flow, a small wake formed:
Cd = ~18.5/Re^0.6

Netwon Flow, max wake:
Cd = ~0.5

Question 14

Stokes flow around a sphere applies up to Reynolds number of:

Answer 14

< 0.2

Question 15

A change in fluid velocity does not influence a body’s drag coefficient

Answer 15

False

Question 16

knots to m/s

Answer 16

1.94 knots = 1 m/s

Question 17

drag force for flow around a sphere, as developed by Stokes

Answer 17

Fd = 3πμdU

Question 18

a sphere is released into a viscous fluid

Answer 18

reaches terminal velocity,
due to the balance of forces

𝐷𝑟𝑎𝑔 𝐹𝑜𝑟𝑐𝑒 + 𝐵𝑢𝑜𝑦𝑎𝑛𝑐𝑦 𝐹𝑜𝑟𝑐𝑒 = 𝑊𝑒𝑖𝑔ℎ𝑡