Moving Fluids - Streamline and Laminar Flow

Question 1

what do drawn streamlines represent

Answer 1

the velocity of a liquid at each point within it

Question 2

how are streamlines drawn

Answer 2

• as arrowed lines

- that show the paths taken by the small regions of the fluid

Question 3

what is laminar flow

Answer 3

when the adjacent layers of air do not cross over each other

Question 4

what is the main characteristic of laminar flow

Answer 4

• there are no abrupt changes in speed or direction

- so the velocity at a point is constant

Question 5

what is turbulent flow

Answer 5

• when layers of fluid cross into each other

- as the fluid swirls around and forms vortices or eddy currents

Question 6

what would the flow of air past a plane wing be like

Answer 6

• the flow from the front of the wing through the back is laminar
• however at the very back of the wing, behind it, there is turbulence

Question 7

how do the flows of a fluid differ according to the speed it is travelling

Answer 7

• slowly flowing water consists of laminar flow

- whereas a lot of turbulence occurs in fast flowing waters

Question 8

what does the rate of flow depend on

Answer 8

• the speed of flow
• the radius of the tube
• the density of the fluid
• the viscosity of the fluid

Question 9

what is the reason for the rate of flow of oil and gas being controlled

Answer 9

• the efficiency of fluid transfer through tubes is greatly reduced if turbulence occurs
• so the rate of flow needs to be controlled so that the critical speed is not exceeded

Question 10

what is viscosity

Answer 10

the thickness or stickiness of a fluid

which therefore relates to its resistance to flow

Question 11

how can the viscosities of fluids be practically compared

Answer 11

• by observing their rates of flow through a glass tube

- a device called a Redwood viscometer can be used

Question 12

what is the flow of a fluid relative to a sphere slowly moving through it

Answer 12

laminar

Question 13

how is viscous drag created during the fall of the sphere

Answer 13

• the molecules of the fluid adhere to the surface of the sphere and move along with it
• creating a viscous drag between the other layers of the fluid

Question 14

what was the equation that was derived to calculate this force, the viscous drag

Answer 14

F = 6 pi n r v

Question 15

what is the name of the equation

Answer 15

Stoke’s Law

Question 16

what do each of the symbols represent in the equation

Answer 16

F = force	
pi = pi (3.14...)	
n (greek letter) = coefficient of viscosity 		
r = radius of sphere
v = velocity relative to the fluid

Question 17

what does stokes law state

Answer 17

• that for a sphere moving through a fluid
• the viscous drag acting on it is given by the equation F = 6 pi n r v
• provided that the movement of the fluid relative to the sphere is laminar

Question 18

what are the three forces a sphere freely falling through a fluid would be subject to

Answer 18

• weight W
• upthrust
• viscous drag F

Question 19

what would the velocity of the sphere initially be like as it is falling through the fluid

Answer 19

• its velocity would be increasing

- as it is accelerating due to gravity

Question 20

what would this mean about the resultant forces acting on the sphere and how would you construct an equation from the three forces acting on it to show this

Answer 20

• the resultant force is not 0 but positive in the downwards direction
• and as weight is the only force acting downwards while viscous drag and the upthrust push it upwards
• Fr = W – (U + F) where W > U + F

Question 21

when does the sphere hit terminal velocity and how can you use the derived equation to show this

Answer 21

• it hits terminal velocity when the weight is equal to the sum of the upthrust and viscous drag
• W = U + F
• this is because at terminal velocity sphere is no longer accelerating but at a constant velocity
• meaning that the resultant force acting on it is 0
• therefore where Fr = W – (U + F), Fr would be 0 when W = U + F

Question 22

what variable in the equation changes and why

Answer 22

• the viscous drag, F
• because in laminar flow, the drag is directly proportional to the velocity of the sphere
• meaning that as the velocity increases, so will the viscous drag until its sum with upthrust equals W

Question 23

what is the relationship between viscous drag and velocity in laminar and turbulent flow

Answer 23

• in laminar flow, the drag is directly proportional to the velocity (d dpt v)
• in turbulent flow, the drag is directly proportional the velocity squared (d dtp v^2)

Question 24

what can be done if you measure the terminal velocity of a sphere falling through a fluid

Answer 24

you can calculate the coefficient of viscosity of the fluid

Question 25

what is the coefficient of viscosity

Answer 25

• the measure of the resistance to flow for a fluid

- it has the units Nsm-2 sometimes changes to Pas

Question 26

if the sphere has reached terminal velocity , what would be the relationship between its weight, the upthrust and the viscous drag

Answer 26

W = U + F

Question 27

what would the weight of the displaced fluid be

Answer 27

• weight = mg
• m(of fluid, f)g = Vp(f)g as mass = volume x density
• volume = 4/3 pi r^3
• so Vp(f)g = 4/3 pi r^3(f)g