Answered: Determine whether the statement is true…

Determine whether the statement is true or false. The continuity equation for incompressible fluids states that the divergence of the velocity vector field of the fluid is zero. True O False

International Edition---engineering Mechanics: Statics, 4th Edition

4th Edition

ISBN:9781305501607

Author:Andrew Pytel And Jaan Kiusalaas

Publisher:Andrew Pytel And Jaan Kiusalaas

Chapter1: Introduction To Statics

Section: Chapter Questions

Problem 1.10P: A differential equation is d2ydt2=Ay2+Byt where y represents a distance and t is time. Determine the...

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Which of the following are true?
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A differential equation is d2ydt2=Ay2+Byt where y represents a distance and t is time. Determine the dimensions of constants A and B for which the equation will be dimensionally homogeneous.
The paragraph below contains more than one instance of false statements or incorrect logic. In a short answer (50 words or less) based on transport and mathematical concepts, describe at least two errors in this paragraph that leads to the faulty conclusion. Consider a gas confined within a large sealed holding tank. Assume that the gas is stagnant (in the continuum sense) so that v = Q everywhere inside the tank. The continuity equation Dp Dp -p(V.v) applies to this gas. Since v= Q the continuity equation reduces to = 0. Dt Dt Integrating this equation gives the result that the density of the gas must be constant at every position inside the tank. Constant density means the gas is incompressible. Since everyone knows gases are actually compressible, the original assumption that y = 0 must be incorrect. Thus, we conclude that it is not possible to have storage tanks full of stagnant gas – there must always be some non-zero velocity.
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3. Discuss the Bernoulli’s theorem 4. Discuss the Continuity equation
Please answer the question. Also provide explanation
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