Explanation Given Information: Rotating fluid engine oil temp, 20 ° c P=Pm everywhere on the free surface, The flow is rotationally symmetric about z-axis Concept used: Euler's equation ζ ( δ u r δ t + u r δ u r δ r + u 0 r δ u r δ θ − u θ 2 r + u z δ u r δ z ) = − δ p δ r + ζ g Calculation: As T = 20 ° , So, the density of engine oil is different. The r component of Euler equation is ζ ( δ u r δ t + u r δ u r δ r + u 0 r δ u r δ θ − u θ 2 r + u z δ u r δ z ) = − δ p δ r + ζ g ................. (1) Where, u r = 0 u z = 0 u 0 = ω r Substituting in equation (1), we get, − δ p δ r = ζ ω 2 r ........................ (2) Now the Z component of Euler's equation is ζ ( δ u z δ t + u r δ u z δ r + u 0 r δ u z δ θ + u z δ u z δ z ) = − δ p δ r + ζ g z ................ (3) Where, u r = 0 u z = 0 u θ = ω r Equation 3 becomes δ p δ z = − ζ g As we express p in function of r and z by cross-integration, integrating Eq

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ISBN: 9781266016042

Author: CENGEL

Publisher: MCG CUSTOM

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Chapter 10, Problem 46P

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An equation for the shape of the free surface where the rotating fluid is water at 20°C.

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Chapter 10, Problem 45P

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Chapter 10 Solutions

FLUID MECHANICS FUND. (LL)-W/ACCESS

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An equation for the shape of the free surface where the rotating fluid is water at 20°C.

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Chapter 10 Solutions