Moving Fluids - Streamline and Laminar Flow Flashcards
what do drawn streamlines represent
the velocity of a liquid at each point within it
how are streamlines drawn
- as arrowed lines
- that show the paths taken by the small regions of the fluid
what is laminar flow
when the adjacent layers of air do not cross over each other
what is the main characteristic of laminar flow
- there are no abrupt changes in speed or direction
- so the velocity at a point is constant
what is turbulent flow
- when layers of fluid cross into each other
- as the fluid swirls around and forms vortices or eddy currents
what would the flow of air past a plane wing be like
- 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
how do the flows of a fluid differ according to the speed it is travelling
- slowly flowing water consists of laminar flow
- whereas a lot of turbulence occurs in fast flowing waters
what does the rate of flow depend on
- the speed of flow
- the radius of the tube
- the density of the fluid
- the viscosity of the fluid
what is the reason for the rate of flow of oil and gas being controlled
- 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
what is viscosity
the thickness or stickiness of a fluid
which therefore relates to its resistance to flow
how can the viscosities of fluids be practically compared
- by observing their rates of flow through a glass tube
- a device called a Redwood viscometer can be used
what is the flow of a fluid relative to a sphere slowly moving through it
laminar
how is viscous drag created during the fall of the sphere
- 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
what was the equation that was derived to calculate this force, the viscous drag
F = 6 pi n r v
what is the name of the equation
Stoke’s Law
what do each of the symbols represent in the equation
F = force pi = pi (3.14...) n (greek letter) = coefficient of viscosity r = radius of sphere v = velocity relative to the fluid
what does stokes law state
- 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
what are the three forces a sphere freely falling through a fluid would be subject to
- weight W
- upthrust
- viscous drag F
what would the velocity of the sphere initially be like as it is falling through the fluid
- its velocity would be increasing
- as it is accelerating due to gravity
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
- 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
when does the sphere hit terminal velocity and how can you use the derived equation to show this
- 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
what variable in the equation changes and why
- 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
what is the relationship between viscous drag and velocity in laminar and turbulent flow
- 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)
what can be done if you measure the terminal velocity of a sphere falling through a fluid
you can calculate the coefficient of viscosity of the fluid
what is the coefficient of viscosity
- the measure of the resistance to flow for a fluid
- it has the units Nsm-2 sometimes changes to Pas
if the sphere has reached terminal velocity , what would be the relationship between its weight, the upthrust and the viscous drag
W = U + F
what would the weight of the displaced fluid be
- 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
