The record-read head for a computer disk-drive memory...

The record-read head for a computer disk-drive memory storage system rides above the spinning disk on a very thin film of air (the film thickness is $0.25 \mu \mathrm{m}$ ). The head location is $25 \mathrm{mm}$ from the disk centerline; the disk spins at $8500 \mathrm{rpm} .$ The record-read head is $5 \mathrm{mm}$ square. For standard air in the gap between the head and disk, determine (a) the Reynolds number of the flow, (b) the viscous shear stress, and (c) the power required to overcome viscous shear.

The record-read head for a computer disk-drive memory storage system rides above the spinning disk on a very thin film of air (the film thickness is $0.25 \mu \mathrm{m}$ ). The head location is $25 \mathrm{mm}$ from the disk centerline; the disk spins at $8500 \mathrm{rpm} .$ The record-read head is $5 \mathrm{mm}$ square. For standard air in the gap between the head and disk, determine
(a) the Reynolds number of the flow,
(b) the viscous shear stress, and (c) the power required to overcome viscous shear.

Key Concepts

Power Dissipation Due to Viscous Shear

In fluid systems, power dissipation due to viscous shear represents the rate at which work is done against viscous forces, leading to energy loss in the system. It is determined by multiplying the shear stress by the sliding velocity and the area over which the shear acts. This concept is central to understanding the energy requirements for maintaining motion in systems where viscous forces play a significant role, such as in thin film fluid layers between moving surfaces.

Viscous Shear Stress

Viscous shear stress describes the force per unit area arising from the fluid's resistance to deformation under a velocity gradient. It is calculated using the fluid’s dynamic viscosity multiplied by the rate of change of velocity with respect to the distance perpendicular to the flow. This concept is fundamental in analyzing the forces acting on surfaces in contact with a moving fluid layer, especially in thin film lubrication applications.

Reynolds Number

The Reynolds number is a dimensionless parameter used in fluid mechanics to compare inertial forces to viscous forces within a flow. It helps determine whether the flow is laminar or turbulent. In problems involving thin films or small gaps, even relatively small velocities might result in low Reynolds numbers, indicating that viscous effects dominate the flow behavior.

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