Flow and Drag

Question 1

What is drag

Answer 1

Forces acting opposite to the relative motion of the object moving through surrounding fluid

Question 2

What is D Alambert’s paradox

Answer 2

Based on calculations an object in steady fluid flow will experience no drag. however an object in steady flow must experience drag because flow is viscid and there will be energy lost due to friction

Question 3

Why did D Alambert calculate that objects in flow will experience no drag

Answer 3

because he assumed inviscid flow: no energy will be lost or gained ; total energy would remain constant ( no friction) and he said there will be no net pressure differences

Question 4

Draw the pressure map experienced by an object in viscid flow

Answer 4

L12 slide 13

Question 5

What is the boundary layer concept

Answer 5

• viscous effects of drag are confined within the boundary layer
• viscosity leads to a steep velocity gradient and high shear forces
• outside the layer viscosity is irrelevant and flow is inviscid

Question 6

Describe what happens to the boundary layer of a moving sphere

Answer 6

1. fluid hits stagnation point, no velocity high static pressure
2. moves up the ball surface, gaining velocity because it is entering a constricted ‘area’ ( so static pressure decreases).
3. favourable pressure gradient allows fluid to flow past ( while offsetting effects due to friction)
4. when we move down the curve, velocity decreases due to frictional loses ( static pressure increases) and the increase in SA (continuity principle)
5. dynamic pressure is converted back to static prssure but there is a loss of fluid momentum due to friction and the unfav. gradient
6. there is an unfavourable pressure gradient. which causes flow to slow: leads to stagnation and flow separation and flow reversal

Question 7

What is frictional drag ?

Answer 7

• occurs tangential to the surface of the object
• occurs as a direct result of viscosity
• arises due to shearing of the fluid in the boundary layer adjacent to the surface
• directly proportional to v

Question 8

What is pressure drag?

Answer 8

• normal to the surface
• indirect result of the viscosity of the fluid reducing the momentum of the fluid
• leads to flow separation
• fluid collides with the plate area and exerts a force proportional to the density of the fluid and the surface area of the plate
• 1/2 * p * S* v^2

Question 9

what is the maximum pressure acting on the object in a flowing medium

Answer 9

it is at the stagnation point where P_max = 1/2 * p * v^2

Question 10

When we plot the pressure difference along an object length – how would we normalize this

Answer 10

y axis: take the dP/ P_max. (P_max= 1/2 * p * v^2) = the pressure coefficient

Question 11

In a pressure coefficient vs length graph where do you expect to find

a. lens/eyes of the fish
b. the gills

Answer 11

a. lens will be found where C_p = 0 because there is no pressure difference for distortion
b. gills found at minimum Cp

Question 12

Given that there is a fish swimming at 2m/s in salt water ( p =1027) what is the pressure gradient flowing through the gills if Cp = -0.4

Answer 12

Because we have to find the pressure gradient from mouth the gills so at mouth Cp =1 ( outermost point)
so we have 1-(-0.4) = 1.4 = dP / P_max

Question 13

At high Reynold’s number what causes drag and what is the significance of drag

Answer 13

• drag is the net force exerted by the fluid on the object
• drag is due to the friction exerted by the fluid as it flows around the object AND the pressure drag due to the pressure differences around the object

Question 14

How does the drag force change with increasing fluid speed

Answer 14

drag force increases ( since drag is proportional to fluid by v^2)

Question 15

How do we standardize the drag force vs velocity graph

Answer 15

plot the coefficient of drag with respect to the Reynold’s number ( the greater the Reynold’s number the greater the drag since high Reynold’s number typically implies more velocity)

Question 16

What is the coefficient of drag

Answer 16

• because drag is force = pressure* are = dynamic pressure * area so we take the drag force/ ( 1/2 * p *v ^2 * A)
• relative amount of drag experienced by an object in a flowing fluid relative to the amount of force exerted directly on some defined area of the object

Question 17

What is the coefficient of drag for a perpendicular plate.

Answer 17

perpendicular plate will not have a flow behind the plate ( so no low pressure turbulent wake is made) will have Cd=1

Question 18

For high drag body what is the area used for coefficient of drag calculations

Answer 18

cross sectional area

Question 19

What is the reference area used for streamlined bodies

Answer 19

wetted area

Question 20

What is the reference area used for objects with wings

Answer 20

planform area

Question 21

What is the reference area used for Cd calc for blimp shaped objects

Answer 21

V^2/3

Question 22

Draw how the coefficient of drag vs Re curve will look like

Answer 22

at low Re there is high viscosity and skin friction fominates
- at high Re pressure drag dominates

Question 23

What is the drag crisis?

Answer 23

The minimum point in the coefficient of drag vs. Re curve.
It is when the boundary layer becomes turbulent upstream such that the boundary layer separates further back leading to a narrow wake and thus less pressure drag

Question 24

Why is there flow separation of the boundary layer

Answer 24

drag present in the boundary layer reduces the momentum of the fluid and causes separation

Question 25

How can we reduce the drag coefficient

Answer 25

Minimize pressure drag

1. fill the space behind a bluff body to delay separation
2. dimpling of the surface to induce turbulence in the boundary layer– increases the momentum exchanged between the high momentum free stream fluid and the no slip condition fluid, this adds momentum to the surface and delays boundary layer separation ( smaller wake = smaller pressure drag)

Question 26

What happens to drag forces at low Re

Answer 26

drag depends solely on the viscous forces ( = uvS/l)

so the drag is proportional to the size and speed of the object ( greater size and speed= slower)

Question 27

Why is a streamline slower than a sphere in low Re than in high Re

Answer 27

low Re: the streamline object has a greater surface area and so it experienes more viscous force than the sphere
high Re: because pressure forces are dominant so the streamline will have a narrow wake ( = less pressure force)

Question 28

if heart volume scales with M, how will heart rate scale with animal mass

Answer 28

the blood volume should increase isometrically (M) while the rate at which heart is pumped should match the metabolic rate (M^2/3) so
blood flow = stroke volume * heart rate
M = M^2/3 * M^x
so M^x = M ^-1/3

Question 29

Draw how the coefficient of drag vs Reynold’s number of a circular disc will look like

Answer 29

at high Re number the pressure drag will be dominant and the only contributing force. because the 1/2 pv^2*A will be the same so that is why it would be fixed at Cd =1 at high Re only ( at low Re it will have experienced frictional forces)

Question 30

Compare the difference between the different drag components of a sphere and streamline body at high Re number

Answer 30

skin drag of sphere &laquo_space;skin drag of streamline body
pressure drag of sphere&raquo_space;»» pressure drag of streamline
so the sum of the pressure drag and skin drag causes
drag exp. by sphere > drag exp. by streamline

Question 31

Given the Re and a Cd vs Re graph how would you find the drag experienced by the object

Answer 31

using Re read Cd off the graph and since Cd = Fd / 1/2pv^2*A we can find the area and backtrack to calculate Fd

Question 32

What happens to the boundary layer if the fluid flow was inviscid

Answer 32

there would be no boundary layer as the no slip condition would not exist