Fluid Mechanics
The inherent characteristic of an equal percentage valve relating flow rate 'q' with valve stem movement 'x' are described by the equation

dq/dx = K/q
dq/dx = K.q
dq/dx = Kq²
dq/dx = K

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Fluid Mechanics
The Prandtl mixing length is

Useful for computing laminar flow problems
Zero at the pipe wall and is a universal constant
Independent of radial distance from the pipe axis
Independent of the shear stress

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Fluid Mechanics
In case of hydraulically smooth pipe, the resistance to flow depends only on the Reynolds number, whereas for a hydraulically rough pipe, the resistance to flow is governed by the relative roughness. Two pipes are said to have the same hydraulic roughness, when they have equal values of

Relative roughness
Absolute roughness
Friction co-efficient for flows at equal Reynold number
All of these

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