GATE CE 2020 Set 2 — Question 34

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NAT+1 / -0EasyBoundary Layer TheoryLaminar & Turbulent FlowWater Resources EngineeringVelocity Distribution

Water Resources Engineering → Laminar & Turbulent Flow → Boundary Layer Theory

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Velocity distribution in a boundary layer is given by uU=sin(π2yδ)\frac{u}{U_\infty} = \sin \left( \frac{\pi}{2} \frac{y}{\delta} \right), where uu is the velocity at vertical coordinate yy, UU_\infty is the free stream velocity and δ\delta is the boundary layer thickness. The values of UU_\infty and δ\delta are 0.3 m/s0.3 \text{ m/s} and 1.0 m1.0 \text{ m}, respectively. The velocity gradient (dudy)\left( \frac{du}{dy} \right) (in s1\text{s}^{-1}, round off to two decimal places) at y=0y = 0, is ________________.
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