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Leakage in narrow clearance, spool valve. Hydraulic clearance. Flow in narrow clearances are of vital importance in hydraulic system 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 pumps, hydraulic motors ...
is the Reynolds number with the cylinder diameter as its characteristic length; Pr {\displaystyle \Pr } is the Prandtl number . The Churchill–Bernstein equation is valid for a wide range of Reynolds numbers and Prandtl numbers, as long as the product of the two is greater than or equal to 0.2, as defined above.
The hydraulic diameter, D H, is a commonly used term when handling flow in non-circular tubes and channels. Using this term, one can calculate many things in the same way as for a round tube. When the cross-section is uniform along the tube or channel length, it is defined as [1] [2] =, where
Where is the dimensionless Strouhal number, is the vortex shedding frequency (Hz), is the diameter of the cylinder (m), and is the flow velocity (m/s). The Strouhal number depends on the Reynolds number R e {\displaystyle \mathrm {Re} } , [ 5 ] but a value of 0.22 is commonly used. [ 6 ]
The size of the largest scales of fluid motion (sometimes called eddies) are set by the overall geometry of the flow. For instance, in an industrial smoke stack, the largest scales of fluid motion are as big as the diameter of the stack itself. The size of the smallest scales is set by the Reynolds number.
Here l is the turbulence or eddy length scale, given below, and c μ is a k – ε model parameter whose value is typically given as 0.09; =. The turbulent length scale can be estimated as =, with L a characteristic length. For internal flows this may take the value of the inlet duct (or pipe) width (or diameter) or the hydraulic diameter.
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L is the length of pipe, μ is the dynamic viscosity, Q is the volumetric flow rate, R is the pipe radius, A is the cross-sectional area of pipe. The equation does not hold close to the pipe entrance. [8]: 3 The equation fails in the limit of low viscosity, wide and/or short pipe.