What are some real world situations which can be usefully modeled by Uniform Random Variables?
Any situation where a range of possible outcomes is considered equally likely is a suitable candidate for the Uniform Random Variable model. Many such situations arise in practice.
Consider throwing a dart at a dartboard in such a way that all points on the board are equally likely. Then the ANGLE of the dart from the x-axis is a random variable which is equally likely to take any value between 0 and 360 degrees.
Consider picking a digit at random from 0,1,2,...,9 in such a way that all ten integers are equally likely. Make your choice the first digit of a decimal. Pick the second digit in the same way. Go on to the third digit and so on. At the n-th stage you will have an n-decimal place accurate real world approximation of a uniform random variable between 0 and 1.
EXCEL generates a uniform random variable. In fact computers are discrete finite state machines and cannot generate continuous random variables. EXCEL actually generates a discrete uniform random variable which is accurate to 15 decimal places. This is close enough to a continuous random variable for practical purposes.