Question

The relative velocity between two layers of fluid, separated by 0.1 mm is 2 cm/s. Calculate the
velocity gradient​

Answer 1

Answer :

• ∆v = 2 cm/s
• They are seperated by 0.1 mm
• Velocity Gradient = ?

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● Velocity Gradient is equal to the date of change of velocity with respect to the distance Fromm some fixed layer

● dv/dx = ∆v/x

Converting Units :

• ∆v = 2 cm/s = 2 × 10 = 20 mm/s

$\displaystyle\:\underline{\bigstar\:\textsf{According to the Question :}}$

$\sf:\implies \dfrac{dv}{dx} = \dfrac{\Delta v}{x}$

• ∆v = 20 mm/s
• x = 0.1 mm

$\sf:\implies \dfrac{dv}{dx} = \dfrac{20}{0.1}$

$:\implies \underline{\boxed{\pink{\mathfrak{\dfrac{dv}{dx} = 200 \ s^{-1}}}}}$

∴ The Velocity Gradient is 200 sec⁻¹

Answer 2

Quєstíσn

The relative velocity between two layers of fluid, separated by 0.1 mm is 2 cm/s. Calculate the velocity gradient.

Answєr

gívєn :-

∆v = 2 cm/s

= 2 mm/s

x = 0.1 mm

sσℓvє :-

Velocity gradient = dv/dx

dv/dx = ∆v/x

dv/dx = 20/0.1

dv/dx = 200/s

Velocity Gradient is 200/s

rєqυírєd αnswєr : 200/s

Answer Completed

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