What is the shear force of a fluid (velocity \(\vec{u}\)) near the wall for a moving wall (velocity (\(\overrightarrow{u_{wall}}\)))?(a) \(\vec{F}=-\mu\frac{\vec{u}}{\Delta y}\times area\)(b) \(\vec{F}=-\mu\frac{\vec{u}-\overrightarrow{u_{wall}}}{\Delta y}\times area\)(c) \(\vec{F}=-\mu\frac{\vec{u}-\overrightarrow{u_{wall}}}{\Delta y}\)(d) \(\vec{F}=-\mu\frac{\vec{u}}{\Delta y}\)This question was posed to me in an internship interview.This interesting question is from Boundary Conditions in chapter Boundary Conditions of Computational Fluid Dynamics

What is the shear force of a fluid (velocity \(\vec{u}\)) near the wal

1.	What is the shear force of a fluid (velocity \(\vec{u}\)) near the wall for a moving wall (velocity (\(\overrightarrow{u_{wall}}\)))?(a) \(\vec{F}=-\mu\frac{\vec{u}}{\Delta y}\times area\)(b) \(\vec{F}=-\mu\frac{\vec{u}-\overrightarrow{u_{wall}}}{\Delta y}\times area\)(c) \(\vec{F}=-\mu\frac{\vec{u}-\overrightarrow{u_{wall}}}{\Delta y}\)(d) \(\vec{F}=-\mu\frac{\vec{u}}{\Delta y}\)This question was posed to me in an internship interview.This interesting question is from Boundary Conditions in chapter Boundary Conditions of Computational Fluid Dynamics
Answer» CORRECT CHOICE is (b) \(\vec{F}=-\mu\frac{\vec{U}-\overrightarrow{u_{wall}}}{\Delta y}\times area\) The explanation: Shear force is a PRODUCT of shear stress and area. Shear stress is defined by NEWTON’s law of viscosity. For moving walls, the relative velocity \(\vec{u}-\overrightarrow{u_{wall}}\) should be taken. Therefore, the shear force is given by \(\vec{F}=-\mu\frac{\vec{u}-\overrightarrow{u_{wall}}}{\Delta y}\times area\).

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