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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.
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 ...
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
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.
In physics, a characteristic length is an important dimension that defines the scale of a physical system. Often, such a length is used as an input to a formula in order to predict some characteristics of the system, and it is usually required by the construction of a dimensionless quantity, in the general framework of dimensional analysis and in particular applications such as fluid mechanics.
A is a reference area, e.g. the cross-sectional area of the body perpendicular to the flow direction, V is volume of the body. For instance for a circular cylinder of diameter D in oscillatory flow, the reference area per unit cylinder length is A = D {\displaystyle A=D} and the cylinder volume per unit cylinder length is V = 1 4 π D 2 ...
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Think of the lamina as a ring of radius r, thickness dr, and length Δx. The area of contact between the lamina and the faster one is simply the surface area of the cylinder: A = 2πr Δx. We don't know the exact form for the velocity of the liquid within the tube yet, but we do know (from our assumption above) that it is dependent on the radius.