effects of the boundary - water

how do flowing fluids exhibit viscous effects?

- stick to solid surfaces

- have stresses within their body

what is shear stress in a fluid proportional to

the velocity gradient, ie the rate of change of velocity across the flow

what is μ for a newtonian fluid?

the coefficient of dynamic viscosity

describe the features of laminar flow

- motion of fluid particles is very orderly

- move in straight lines

- parallel to pipe wall

describe the features of turbulent flow

- motion is locally completely random

- over all direction in one way

what is reynold's number?

what can reynold's number predict?

change from laminar to turbulent flow for any fluid

what are the reynold's numbers for laminar flow?

Re < 2000

what are the reynold's numbers for transitional flow?

2000

what are the reynold's numbers for turbulent flow?

Re>4000

what are the SI units for reynold's number?

it is a non-dimensional number

what would limiting velocities be in a typical central heating system pipe (diameter 0.015m)?

0.0733 and 0.147 m/s (very slow)

where does laminar flow rarely occur?

in piped water systems

where does laminar flow more commonly occur?

in fluids of greater viscosity (eg in bearing with oil)

what does the Reynold's number mean?

Re = inertial forces / viscous forces

where do inertial forces dominate?

in faster flow

larger Re = turbulent flow

where do viscous forces dominate?

in slower flow

smaller Re = laminar flow

summarise the key features of laminar flow?

- Re<2000

- low velocity

- dye does not mix with water

- fluid particles move in straight lines

- simple analysis possible

- rare in practice in water systems

summarise the key features of transitional flow?

- 2000< Re < 4000

- medium velocity

- dye stream wavers - mixes slightly

summarise the key features of turbulent flow?

- Re>4000

- high velocity

- dye mixes rapidly and completely

- particle paths completely irregular

- average motion is in flow direction

- cannot be seen by naked eye

- must measure using laser

- analysis difficult

what is the most common type of flow?

turbulent flow

how do the effects of friction present in fluids?

as a pressure loss

what does shear stress do in a real flowing fluid?

slows the flow

how can we view pressure loss?

attach a manometer

pressure at 1 is greater than pressure at 2

difference is Δp

how can we find driving force due to pressure?

driving force = upstream force - downstream force

= pA - (p-Δp)A=ΔpA

how can we find retarding force due to shear stress at wall?

retarding force = shear stress x area acts

= τw x area of pipe wall

what does driving force equal?

retarding force

what is pressure loss proportional to?

velocity and laminar flow

pressure loss is proportional to velocity and laminar flow, what does this confirm?

- fluid does not slip past a boundary

- newton's law of viscosity

what is the Hagen-Poiseuille equation?

fluid flowing over a stationary surface is brought to rest by what?

shear stress τo

describe typical flow over a flat plate

upstream, before plates have free stream and constant velocity

downstream after flowing along the plate, the velocity profile that exists does not change - fully developed