Question

1. If an ideal solution of the flow field through a nozzle is shown with a depiction of vectors distributed at points throughout the nozzle that illustrate the magnitude and direction of steady flow through those points, this depiction would be Eulerian or Lagrangian (circle one)

2. If an ideal solution of the flow field through a nozzle is shown with a depiction of vectors attached to particles moving through the nozzle, changing magnitude and direction as they move through the nozzle, this depiction would be Eulerian or Lagrangian (Circle one) Consider streamlines, pathlines, and streaklines for the following fill-in-the-blanks statements

3 through 6:

3. ____________________, __________________ and _________________ are coincidental for ______________, ___________________ flow.

4. A stream of particles passing through a point would form a __________________, even if they weren’t all following the same path.

5. For an unsteady flow, the __________________ seen in #4 would not coincide with ___________________ or ________________.

6. A time exposure photograph of a visible moving flow particle would show a __________________ of the particle.

7. The tangent to flow at a point along a _____________________ can be determined as the ratio ____/____ or ____/____ and this relationship can be used to form the differential equation used to find the equation of a ____________________ passing through that point.

8. Flows are broadly classified by frictional effects (viscous effects) as either _______________ or ______________, or sometimes as ______________ between these classifications.

9. Flow dominated by viscosity travels in straight pathlines and is considered _________________, and flow develops into ______________ velocity profiles.

10. Flow that is erratic and mixing with particles that do NOT follow any particular pathlines would be considered _______________, and the flow has only a slight ___________ ____________ near walls or boundaries.

11. Non-dimensional flow is considered ______________ flow while one-dimensional flow for example only varies with ________________.

12. A flow is ____________ if it does not vary with time and ________________ if it does not vary with position.

13. If a heat source is allowed to reach thermal equilibrium with fluid flowing past it, a thermal image can reveal the variation of temperature with position, and also indicate when the flow through the region has reached equilibrium. There would be a local change in the rate of heating of a particle (change of Temperature with time) in the flow field if the __________ was unsteady (time dependent). There will be a convective change in the rate at which particles would be heating due to the heat distribution and the velocity distribution through the region. Identify and plainly label the terms associated with the LOCAL (circle these terms) and CONVECTIVE (box these terms) rates in each of the four expressions at right.

14. The expression shown in the illustration of #13 is the _______________ or ________________ derivative.

15. It is essential to know and recognize standard forms of equations of circles, lines, parabolas, hyperbolas and the like. Identify the following geometric forms: Y = mx + b _______________ xy = C ________________ y = ax2__________________ Such equations often become families of curves known as _______________ used to illustrate flow patterns, and these equations are determined by method of #7.

16. Euler’s Equations are derived by summing forces in the ________________ and _______________ directions relative to a streamline. When forces are unbalanced, a flow may be accelerating in the __________________ direction (streamlines converging), or accelerating in the _____________ direction (with streamlines curving) or both.

17. Regarding Euler’s EoM valid only along A streamline, give three additional restrictions to the use of these differential equations of motion. __________________, ___________________, and _____________ ______________ in the normal direction.

18. Two important applications of Euler’s EoM to horizontal ideal fluid flow indicate that horizontal pressure is ______________ along a streamline and that variation of pressure vertically is _________________.

19. Vortical motion is generally classified by more than the two distinct types, illustrated at right. Give examples of each of these types of flow, and identify one more general type. (a) (b)

20. The Bernoulli equation (BE) is obtained by __________________ the Euler equation of motion between two points along a ________________ and is subject to the same restrictions as the Euler EoM.

21. Give five reasons the BE cannot be used as illustrated on the figure at rig

22. To be used as the energy equation for steady flows of incompressible fluids through pipes, terms must be added to the Bernoulli Equation to account for _________ head, ____________ head or head ________ through the pipe system. Show the Bernoulli Equation below with those terms added, and clearly label all terms. Identify those that take place within the control volume and those that occur at control surfaces through which flow occurs.

23. The first law of Thermodynamics relates changes in ___________________ energy,( ) to ______________ added or subtracted from a system or ____________ lost or gained by the system. (Give examples of these two changes.)

24. Give the form of the energy equation for one-dimensional steady flow applied to both compressible and incompressible fluids, and identify each term of the equation.

25. Give the form of the energy equation for compressible flow using enthalpy and explain/identify each term.

26. The energy equation will be identical to the Bernoulli Equation under what three conditions?

Answer 1