Hydraulic clearance. Flow in narrow clearances are of vital importance in

hydraulic system Hydraulics (from Greek: Υδραυλική) is a technology and applied science using engineering, chemistry, and other sciences involving the mechanical properties and use of liquids. At a very basic level, hydraulics is the liquid counter ...

component design. The flow in a narrow circular clearance of a spool valve can be calculated according to the formula below if the height is negligible compared to the width of the clearance, such as most of the clearances in

hydraulic pump Hydraulic pumps are used in hydraulic drive systems and can be hydrostatic or hydrodynamic. A hydraulic pump is a mechanical source of power that converts mechanical power into hydraulic energy ( hydrostatic energy i.e. flow, pressure). It generat ...

hydraulic motor A hydraulic motor is a mechanical actuator that converts hydraulic pressure and flow into torque and angular displacement (rotation). The hydraulic motor is the rotary counterpart of the hydraulic cylinder as a linear actuator. Most broadly ...

s, and

spool valve Spool may refer to: *Bobbin, a cylinder or reel on which a quantity of thread, yarn or wire is wound for use in a particular machine or device * Cable reel, used to carry various types of electrical wires * Spool (record label), active 1998–2008 ...

s. Flow is considered to be laminar. The formula below is valid for a spool valve when the spool is steady. Concentric spool/valve housing position i.e. the height/radial clearance c is the same all around: Units as per SI conventions : Flow Q_i = (∆P · π · d · c³) ÷ (12 · ν · ρ · L) where:
Q = volumetric flow rate (m^3/sec)
ΔP = P1-P2 = pressure drop over the clearance (N/m^2, Pa)
d = valve spool diameter (metre)
c = clearance height (radial clearance) (metre)
ν = kinematic viscosity for the oil (m^2/sec)
ρ = density for the oil (kg/m^3)
L = clearance length (metre) As can be seen from the formula, the clearance height c has much more influence on the leakage than the length. The formula clearly hints of pure laminar flow conditions. It is also valid for gases. Contact between the spool and the wall, the value that is generally used for practical calculations: Flow Q_e = 2.5 · Qi

References

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