Given an incompressible 2d flow with x and z velocity given by u= alpha*x and w= beta* z
a) how are alpha and beta related?
b) if the initial positions (t=0) are given by x and z what are the fluid positions x, z in terms of x, z,t?
c) sketch the x, z fluid element trajectory d) express the velocity field in lagrangian coordinates.

Car batteries are often rated in amp-hours. this rating indicates the quantity of charge that can pass through the battery before the battery's chemical energy must be restored by the car's generator or some other source. the amp-hour unit is convenient for simple calculations. for example, a 60-amp-hour battery can supply a current of 1.0 a for 60 h (or 60 a for 1.0 h) before going dead. find the energy stored in the following. (a) a 58 a-h, 10 v car battery(b) a 1.3 a-h, 1.7 v flashlight battery