To understand thermal linear expansion in solid materials. most materials expand when their temperatures increase. such thermal expansion, which is explained by the increase in the average distance between the constituent molecules, plays an important role in engineering. in fact, as the temperature increases or decreases, the changes in the dimensions of various parts of bridges, machines, etc., may be significant enough to cause trouble if not taken into account. that is why power lines are always sagging and parts of metal bridges fit loosely together, allowing for some movement. it turns out that for relatively small changes in temperature, the linear dimensions change in direct proportion to the temperature. for instance, if a rod has length l0 at a certain temperature t0 and length l at a higher temperature t, then the change in length of the rod is proportional to the change in temperature and to the initial length of the rod: l−l0=αl0(t−t0),orδl=αl0δt.

Two horizontal plates with infinite length and width are separated by a distance h in the z direction. the bottom plate is moving at a velocity u. the incompressible fluid trapped between the plates is moving in the positive x-direction with the bottom plate. align gravity with positive z. assume that the flow is fully-developed and laminar. if the systems operates at steady state and the pressure gradient in x-direction can be ignored, do the following: 1. sketch your system 2. identify the coordinate system to be used. 3. show your coordinates and origin point on the sketch. list all your assumptions. 5. apply the continuity equation to your system. nts of navier stokes equations of choice to your system 7. solve the resulting differential equation to obtain the velocity profile within the system make sure to list your boundary conditions. check units of velocity 8. describe the velocity profile you obtain using engineering terminology. sketch that on the same sketch you provided in (1). 9. obtain the equation that describes the volumetric flow rate in the system. check the units.

15. give an example for some particles or waves that are moving faster than light in everyday life 16. what is a laser? 17. what is an oscilloscope? 18. what does it means practically that nothing is faster than light in vacuum? 19. what is vacuum?

Aplane travels 1000 miles in 5 hours .what is the planes average speed?