Chapter 5, Problem 14P

2. In class, we discussed several different flow scenarios for which we can make enough assumptions to simplify the Navier-Stokes equations enough to solve them and obtain an exact solution. Consulting the cylindrical form of the Navier-Stokes equations copied below, please answer the following questions. др a 1 a + +0x- + +O₂ = Pgr + μl 18²v, 2 ave ²v₁] az2 + at or r de r Əz dr ar Vodvz др [18 + + +Or + +Vz = Pgz +fl at ar r 20 ôz ôz dr ave дов V,Ve ave +Or + + = pge at dr r 80 Əz + az2 a.) In class, we discussed how the Navier-Stokes equations are an embodiment of Newton's 2nd law, F = ma (where bolded terms are vectors). Name the 3 forces that we are considering in our analysis of fluid flow for this class. др a 10 1 ve 2 av 2200] + +μ or 42 30 b.) If we make the assumption that flow is "fully developed" in the z direction, which term(s) would go to zero? Write the term below, describe what the term means in simple language (i.e. do not simply state "it is the derivative of a with…

1. Consult the form of the x-direction Navier-Stokes equation below that we discussed in class. (For this problem, only the x direction equation is shown for simplicity). Note that the equation provided is for a Cartesian coordinate system. In the spaces below, indicate which of the following assumptions would allow you to eliminate a term from the equation. If one of the assumptions provided would not allow you to eliminate a particular term, write "none" in the space provided. du ди at ( + + + 매일) du ди = - Pgx dy др dx ²u Fu u + fl + ax2 ay² az2 - дх - Əz 1 2 3 4 5 6 7 8 9 Assumption Flow is in the horizontal direction (e.g. patient lying on hospital bed) Flow is unidirectional in the x-direction Steady flow We consider the flow to be between two flat, infinitely wide plates There is no pressure gradient Flow is axisymmetric Term(s) in equation

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