Question

Question 1. Willy Wonka's chocolate factory is having a serious problem with inefficiencies in their chocolate syrup routing system. To address this issue, Mr Wonka has asked your engineering geology firm to undertake a study of the components of flow energy in their syrup routing pipe Given the hydraulic head information in Figure 1 computer the items in Table 1. You may assume that this is quite watery syrup (another issue, to deal with at a later date) with a density of 1000 kg m" and that we are on earth (i.e., g = 9.81 m s-1). Total hydraulic Pressure Elevation Velocity Fluid Fluid velocity Elevation head [m) head [m) head [m] head m] pressure [Pal ms Point A Point B Table 1. Components of hydraulic head to be calculated. Figure 1. Schematic diagram of syrup flow through a pipe equipped with (straight pipes) and Pitot tubes (curved pipes). Elevations are indicated by z measurements, and syrup levels are shown by horizontal black lines. Point B piezometers Point A ET Datum, z = 0 m "Note: not to scale Question 2. Is energy conserved in this system? How do you know? If not, where did that energy go? Question 3. Which way is the syrup flowing? How do you know? Question 4. Assume that the along-pipe distance is 100 m and that the circular pipe has a radius of 0.564 m. If this pipe were now filled with fine sand, such that Darcy's Law accurately describes syrup flow, calculate syrup discharge (units of m3 s) through the pipe. Assume the sand has a typical hydraulic conductivity for fine sand ofk = 1 x10" m s-1. Note the velocities we calculated in Question 1 will no longer apply after filling the pipe with sand.
Please help me on question 1

Answer 1

We know that, a piezometer measures piezometric head, i.e (pressure head + datum head), if measured form datum. And, pitot tube will give the stagnation pressure at that point, i.e. (velocity head + datum head). \r\n velocity head = (v^2/2 g) s = 1000 kg/m^3 g = 9.81 m/s^2 pressure head = (p/s g)