Prandtl one-seventh power law

This equation is sometimes referred to as the Prandtl one-seventh power law. 

On the assumption that the velocity profile in a fluid in turbulent flow is given by the Prandtl one-seventh power law, calculate the radius at which the flow between it and the centre is equal to that between it and the wall, for a pipe 100 mm in diameter,... 

The Prandtl one-seventh power law gives the velocity at a distance y from the wall, ux, as ... 

The velocity of the fluid may be assumed to obey the Prandtl one seventh power law, given by equation 11.26. If the boundary layer thickness S is replaced by the pipe radius r, this is then given by ... 

A simple approximate form of the relation between u+ and y+ for the turbulent flow of a fluid in a pipe of circular cross-section may be obtained using the Prandtl one-seventh power law and the Blasius equation. These two equations have been shown (Section 11.4) to be mutually consistent. 

Water is flowing through a 150 mm diameter pipe and its flowrate is measured by means of a 50 mm diameter orifice, across which the pressure differential is 2.27 x 104 N/m2. The coefficient of discharge of the orifice meter is independently checked by means of a pitot tube which, when situated at the axis of the pipe, gave a reading of 100 mm on a mercury-under-water manometer. On the assumption that the flow in the pipe is turbulent and that the velocity distribution over the cross-section is given by the Prandtl one-seventh power law, calculate the coefficient of discharge of the orifice meter. 

Show that, if the Blasius relation is used for the shear stress R at the surface, the thickness of the laminar sub-layer Sb is approximately 1.07 times that calculated on the assumption that the velocity profile in the turbulent fluid is given by Prandtl s one seventh power law. 

Prandtl s one-seventh power law A relationship used to determine the velocity distribution for turbulent flow in pipes carrying fluids given as ... 

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