Velocity
The velocity of hydraulic fluid through a conductor (pipe, tube or hose) is dependent on flow rate and
cross sectional area. Recommended fluid velocities through pipes and hoses in hydraulic systems are as
follows:
Service Velocity (ft/sec) Velocity (m/sec)
suction/intake 2 - 4 0.6 – 1.2
return 4 – 13 1.5 - 4
pressure/discharge 7 - 18 2 – 5.5
Use values at the lower end of the range for lower pressures or where operation is continuous. Refer to
the flow/velocity nomograms on pages four and five for more information, alternatively, fluid velocity
can be calculated using the following formula:
v = Q × 0.408
D²
Where
v = velocity in feet per second (ft/sec)
Q = flow rate in US gallons per minute (USgpm)
D = inside diameter of pipe or hose in inches (in)
In metric units
v = Q × 21.22
D²
Where
v = velocity in metres per second (m/sec)
Q = flow rate in litres per minute (L/min)
D = inside diameter of pipe or hose in millimetres (mm)
Pressure drop
Friction between the fluid flowing through a conductor and its inside wall causes losses, which are
quantified as pressure drop. Pressure drop in conductors is an important consideration for the designer
especially in systems where long pipe or hose runs are necessary. The pressure drop over a length of
pipe or hose can be calculated using the following formula, which for ease of calculation uses metric
units. Before proceeding to the pressure drop calculations, the following variables need to be known:
Flow rate in litres per minute (L/min) Q
Inside diameter of pipe or hose in millimetres (mm) D
Kinematic viscosity of fluid (at operating temperature) in centistokes (cSt) ν
Density of the fluid in kilograms per cubic metre (kg/m³) ρ
Length of the pipe, tube or hose in metres (m) L
1. Calculate fluid velocity:
v = Q × 21.22
D²
Where
v = velocity in metres per second (m/sec)
Q = flow rate in litres per minute (L/min)
D = inside diameter of pipe or hose in millimetres (mm)
2. Calculate the Reynolds Number (Re):
Re = 1000 × v × D
ν
Where
Re = Reynolds Number
v = velocity in metres per second (m/sec)
D = inside diameter of pipe or hose in millimetres (mm)
ν = kinematic viscosity of fluid (at operating temperature) in centistokes (cSt)
3. Calculate the friction factor (f)
The formula used to calculate the friction factor is dependent on the magnitude of the Reynolds
Number.
If the Reynolds Number is less than 2300, flow is laminar and the following formula is used to
calculate the friction factor:
f = 64
Re
Where
f = friction factor
Re = Reynolds Number < 2300
If the Reynolds Number is between 2300 and 4000, flow is transition and greater than 4000 flow is
turbulent. For Reynolds Numbers greater than 2300 and less than 100,000 the following formula can be
used to calculate the friction factor:
f = 0.3164 × Re - 0.25
Where
f = friction factor
Re = Reynolds Number > 2300 and < 100,000
In instances where the Reynolds Number is greater than 100,000, friction is highly dependant on the
roughness of the conductor’s inner surface. In these cases Colebrook’s equation, which considers pipe
roughness, is used to calculate the friction factor. However, due to the relatively low fluid velocities
and high fluid viscosities present in hydraulic systems, Reynolds Numbers of this magnitude should not
be encountered.
4. Calculate the pressure drop:
Finally, pressure drop can be calculated using the following formula:
Δp = v² × f × L × ρ
2D
Where
Δp = pressure drop in Pascals (Pa)
v = velocity in metres per second (m/sec)
f = friction factor
L = length of pipe or hose in metres (m)
ρ = density of the fluid in kilograms per cubic metre (870-890 kg/m³ for hydraulic oil)
D = inside diameter of pipe or hose in metres (m)
Conversions
SUS (32 – 99) cSt = 0.2253 × SUS – (194.4 ÷ SUS)
SUS (100 – 240) cSt = 0.2193 × SUS – (134.6 ÷ SUS)
SUS (> 240) cSt = SUS ÷ 4.635
US gallon × 3.785 = litre
inch × 25.4 = millimetre
inch × 0.0254 = metre
feet × 0.3048 = metre
lb/ft³ × 16.02 = kg/m³
Pascal (Pa) ÷ 100000 = bar
Pascal (Pa) × 0.000145 = psi
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