ENU 4134 – Homework Assignment #0 – Fall 2011 – D. Schubring 1 These are ENU 4133 and/or EML 4140 problems. Do not turn in. Solutions on website. Task 1. The Navier-Stokes Equation Write down the Navier-Stokes equation in vector form and explain the physical signiﬁcance of each term. Assume constant density and a Newtonian ﬂuid with constant viscosity. Task 2. Tube Flow A fully-developed, steady, laminar ﬂow (water at 20 ◦ C and 101 kPa) forms in a round tube of diameter 1 cm. The total pressure gradient (dP/dz) is -10 Pa m-1 . There is no body force. a. Starting from an appropriate form of the Navier-Stokes equation(s), calculate v z ( r ) (that is, the velocity proﬁle in the tube). b. Compute the average velocity and total mass ﬂow rate in the tube. c. Determine from these results if the ﬂow is really laminar. d. Explain what would change in the system if the pressure gradient were to rise to -100 Pa m-1 . Task 3. Conduction
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