Answer to Question #169580 in Mechanical Engineering for nikko

Question #169580

Determine the viscosity, in Pa-s, in between plates that has a 0.5 mm gap with each other. The moving plate travels at 0.50 m/s, relative to the stationary plate, under a shear stress of 4.0 Pa


1
Expert's answer
2021-03-09T04:54:34-0500

Gap: "dy=0.5\\ mm=5\\times10^{-4}\\ m"

Velocity of upper plate: "u=0.50\\ m\/s"

Shear stress: "\\tau=4.0\\ Pa"

Let the fluid viscosity between the plates be "\\mu." We have


"\\tau=\\mu\\dfrac{du}{dy}"

"du=u-0=0.50\\ m\/s"

Then

"\\mu=\\dfrac{\\tau}{\\dfrac{du}{dy}}"

"\\mu=\\dfrac{4.0\\ Pa}{\\dfrac{0.50\\ m\/s}{5\\times10^{-4}\\ m}}=4\\times10^{-3}\\ Pa\\cdot s"


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