Fluid Systems Flashcards
What is a fluid system
A system using confined pressurized fluid with a transmitted force to generate work done.
Purpose of a fluid system.
To transmit power is primary function. lubricant, cooling also
Types of Fluid systems
Hydraulic - liquid (usually oil)
Pneumatic - Inert gas/ air
Fluid system pros
High bandwidth
No complex system E.g no gears
Smooth & compact
No wear/less breakage
High speed/force/power
Can be finely controlled/no slack
Uniform & flexible
Fluid system cons
Can leak at seals/connections
Needs heavy/noisy pump
Cavitation = leads to loss of precision
Contamination = filtration needed
Chemical action = corrosion a
Fluid needs to be positively confined in system
What type of variable is pressure?
Across
Absolute vs Gauge vs Differential pressure
Absolute = measured in respect to perfect vaccum.
Gauge = measured in respect to atmospheric pressure
Differential = difference of pressure between two specified points
Pressure equation
P = force/area
Pressure conversions
1 psi = 6895 pa
Patm = 101325 pa
What type of variable is Flow?
Through
Volumetric vs Mass vs Velocity flow (3 definitions of flow)
Volumetric = measures
volume of flow passing point per unit time.
Mass = measures mass of flow passing point per unit time
Velocity = measures linear speed of fluid per unit time
Flow conversions
1 gpm = 15850 m^3/s = 0.264 Ipm
1 m^3/s = 0.0000631 gpm = 0.0000167 Ipm
Flow equations
Q = A x V
V = avg velocity
Qm = m./ρ
m. = mass rate
ρ = density
Flow: Hydraulic vs Pneumatic
Hydraulic = generally treated as incompressible (density is constant)
Pneumatic = mass flow rate (Qm) is used as flow variable
Flowmeters
Contact = restricts flow, used in careful systems where small pressure drop matter
Contactless
Power equation
power = P x Q
P = pressure
Q = flow rate
Efficiency = power output/ power input
Power conversions
1 watt = 746 hp = 0.293
1 hp = 0.00134 watt
1 Btu/hr = 3.413 watt
Power definition
Rate at which work is done.
Work done = amount of force needed for object to move set distance.
Density definition
How close particles are packed in a substance.
Mass per unit volume.
Density Equation
ρ = m/V
=mass/ Volume
Note: Temp affects density but not mass
Specific gravity definition
Used to determine relative lightness of material compared to water. Relative density.
Note: both density and specific gravity are independent of size.
Specific gravity equation
SG = ρsubstance/ ρwater
p = density
<1 = lighter than water
1> = heavier than water
Viscosity definition
Resistance to flow.
Note: Temp affects viscosity, as temp in increases viscosity decreases
Viscosity in hydraulic systems
Needs to be compromise
If viscosity too high = difficult to push through pipes/fitting = loss of mechanical efficiency
If viscosity too low = fluid leaks by internal seals = loss in volumetric efficiency
Dynamic/Absolute viscosity definition
Resistance to flow/shear of fluid. Measured by placing fluid in between two plates + shearing.
Dynamic viscosity (μ) equations
τ = F/A = μ ΔV/Δy
SI units (Pa-s) but more common unit id cP (centipoise)
1cP =0.001 Pa-s
Dynamic viscosity of water at 20c is 1 cP
Kinematic viscosity definition (ν)
Kinematic viscosity is the dynamic viscosity measured with respect to density. Ratio of the two.
Can be measured by by the time it takes to flow through a capillary.
Kinematic viscosity equation (ν)
ν = μ/ρ
μ = Absolute/dynamic viscosity
ρ = density
SI units (m^2/s) but more common unit id cSt (centistoke)
1 m^2/s = 1.0 x 10^6 cSt
Kinematic viscosity of water at 20c is 1 cSt
Bulk modulus definition
The pressure needed to cause a given decrease in volume of a fluid. “Springiness of fluid.”
Bulk modulus equation
β =ΔP/(ΔV/V)
ΔP = pressure change
(ΔV/V) = change in volume/original volume.
Typical oil will decrease 0.5% for every 1000psi increase
Pascals law
In a confined fluid at rest, pressure acts equally in all directions and acts perpendicular to the walls.
P= F/A
P1 x V1 = P2 x V2
Pascals law: Static pressure
Static fluid pressure doesn’t depend on shape, total mass or surface are of liquid.
Pfluid = F/A = m.g/A —> p = m/V
Pfluid = ρVg/A —> ρgh
P = Patm + Pfluid
Boyles Law
In a closed container with a given number of molecules as the volume decreases particle per unit volume increases = more collisions = greater pressure.
Note temperature and
mass must be constant.
Boyles law equation
P ≈ 1/V —> P1V1 = P2V2
Charles law
If pressure is constant, fluid expands when heated. When temp rises, molecules move faster and collides more, with more force. To keep the mass and pressure constant, volume must increase
Charles law
V ≈ T —> T1/V1 = T2/V2
ΔV = V2 - V1 = V1 x (T2 - T1)/ T1
V2 = V1 + ΔV = V1 + V1/T1 (T2 - T1)
Gay Lussacs Law
If the volume is kept constant during temperature rise = results in the following formula for pressure increase:
P1/T1 = P2/T2 = P3/T3 = constant
General gas equation
For a given mass of gas, pressure and volume divided by absolute temp is constant.
(P1 x V1)/ T1 = (P2 x V2)/ T2
Bernoullis principle
Within a flowing fluid, increase/decrease in speed occurs simultaneously with the increase/decrease in pressure. Increase in speed = decrease in pressure.
When a fluid goes through a narrow space = goes faster
Bernoullis Principle Equation
P1 + 1/2Pv1^2 + Pgh1 = P2 + 1/2Pv2^2 + Pgh2 =
P1 = pressure energy
1/2PV1^2 = Kinetic energy
Pgh1 = Potential energy
For actual rather than ideal flow
P1/Pg + V1^2/2g + h1 * Ha = P2/Pg + V2^2/2g + h2 + He + Hl
Hl = energy lost
He = Heas of energy ecxtracted
Ha = Head energy by pump
Flow velocities
At low velocities flow = smooth and uniform
At high velocities flow = turbulent
Flow velocity & Reynolds number
Laminar flow Re < 2300
Turbulent flow Re > 4000
Transitional flow 2300 < Re > 4000
Fluid energy loss
Flow of fluid through hoses, pipes, fittings etc can result in energy losses due to:
Internal fluid friction
Friction against wall
Orifice drag
Higher friction = efficiency loss
Reynolds number equation
Re = ρVD_h/μ = VD_h/ν
For non circular pipes:
D_h= 4A/S
V = fluid velocity
D_h = Hydraulic diameter
S = perimeter
Reynolds’s number flow
High are - Inertia predominant force, inertia promotes turbulent flow
Low Re - Viscosity predominant force, viscosity promotes turbulent flow
Reynolds’s number definition
Re defines fluid flow and relates viscosity, density and fluid velocity to size. (Non dimensionless ratio of inertia/ viscous forces)
Pressure losses
When fluid is pumped through a system, certain amount of energy is lost due to friction.
Fluid particles rub against pipe = frictional loss.
Rate of shear and heat generated are greatest near the wall + this is where most of the energy transfer occurs
Major losses definition
Occurs when the fluid flows through pipes, hoses, tubing etc and is calculated for the length of the pipe
Minor losses
Occur at valves, fittings, bends, enlargements, contractions, orifice. Converted to loss through equivalent length of pipe
Major losses equation
hf = f L/D V^2/2g —> ΔP = f ρL/2D V^2
L/D = ratio of pipe
V^2/2g = velocity of head
f = friction factor
V^2 = avg flow velocity
D = diameter
L = conduit length
ΔP = pressure drop
Major losses: Friction factor
Laminar flow Re <2100/2300
f = 64/Re
Turbulent flow
smooth pipes
f = 0.316/Re^0.125
Rough pipes (approximation)
f= 0.25/ [log10(ε/3.7D + 5.74/Re^0.9)]^2
Minor losses - K values explained
Pressure drops as fluids undergo sudden expansion/contractions/ flow through pipe fittings, valves, & bends
The pressure loss associated w Bernoullis equation + defined as no. of velocity heads lost due to friction
Velocity heads: energy associated w fluid velocity.
When friction some energy lost and k values represent how much energy lost for that component.
Minor loss - K values equation
hf f = K(V^2/2g) —> ΔP = K (ρ/2)V^2 = K (ρ/2A^2) Q^2
K values - Enlargement/Reduction
Enlargement
K = (1 - (D1/D2)^2)
Reduction
K = 0.5(1 - (D1/D2)^2)
Fittings + bends
K = ft (L/D)
ft = friction factor in turbulent range
L = Length of fitting
D = Inside diameter of fitting
Minor losses - Equivalent length
Minor losses are independent of Reynolds number and can be described as the loss through equivalent length of a straight pipe.
Don’t need to remember following:
hf = f (L/D) (V^2)
hff = K (V^2/2g)
hff = hf so —-> L = D (K/f)
Minor losses - C coefficients
3rd type of pressure loss = comes from flow of fluid through destructed orifices & short tube & some fittings
Minor losses - C coefficients equation
Theoretical velocity of free stream emitted horizontally from bottom of a tank = V = sqrt(2gh)
Friction losses are incorporated as discharge coefficient of velocity so:
V= cd (sqrt(2gh)) —> Q = ACd(sqrt(2gΔh) = ACd(sqrt (2ΔP/ρ)
Fluid question equations to remember
Re (Reynolds no.) = VD/ν
V = Q/A where A = (D/2)^2 x π
ν = kinematic viscosity
Pressure drop =
ΔP = f x ((ρxL)/2D ) xV^2
Or
ΔP = 1/2ρ( v1^2 x v2^2)
