Advanced Fluid Mechanics

Winter Quarter 2020

Stefan LLEWELLYN SMITH
EBUII 574
x23475
http://mae.ucsd.edu/~sgls

Homework IV

Due

Friday February 7, 2020, in class (or before).

Problems (MYO is the textbook; 8th edition)

  1. MYO 8.74
  2. MYO 8.78
  3. MYO 8.96
  4. MYO 8.105
  5. MYO 8.115
  6. MYO 8.119
  7. MYO 8.129
  8. Write a paragraph about the engineering of pipeline design (e.g. petroleum, crude oil). Try and find a specific example to discuss. Cite your sources.

Comments

This homework covers Sections 8.5 and 8.6 of the book.

There isn't much to write about this homework, which is mostly examples. The theoretical background was introduced earlier. The applications here span quite a wide range. Remember that there are 3 basic types of problems: Type I in which you have to find the pressure drop (or sometimes pump power which is related to pressure drop), Type II in which you have have to find the velocity or flow rate, and Type III in which you have to find the pipe diameter. (There are other twists, such as finding viscosity or density, but those are rare.)

Type I is straightforward: from V (sometimes from Q), D (which may be the hydraulic diameter if the pipe is not circular in cross section) and the fluid properties, find Re. That tells you if the flow is laminar or turbulent. If the flow is laminar, use f = 64/Re if it is circular or the appropriate formula if it is not. If the flow is turbulent, use the roughness and Re to find f using the Moody chart or one of the formulas. From f, you can find the major losses. Compute the minor losses and then use the energy equation to find the pressure drop (or shaft work).

For Types II and III, write down the equations you have, which are usually the energy equation and the definition of the Reynolds number in terms of your unknown, either V or D (for Type III the nondimensional roughness is also unknown). Then seek a value for f that satisfies all the equations, either iteratively using the Moody diagram or finding the appropriate solution for f in the Colebrook (or some other) formula, again using iteration or a numerical root finder.

The next section of the class considers external flows. The challenge here is that at high Reynolds numbers we know that the viscous term is small. However, it can't be ignored next to boundaries because of the no-slip condition. This leads to the existence of boundary layers, which are narrow regions over which the flow adjusts to match the free-stream velocity. We need to understand these to obtain the drag due to shear stresses on the boundary. There is also a second challenge: to compute the total drag on a body, which depends on the overall flow field: bodies have a wake behind them which has an important effect on the drag. Turbulence is once again an important issue here. We will use dimensional analysis again to obtain a non-dimensional measure of drag, the drag coefficient.

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