CHAPTER 1  >  ACTIVITIES  >  PROBLEMS  >  PROBLEM 6
Discharging a water tank: A dynamical model
A straight walled tank is filled with water. At the bottom, a horizontal glass pipe with a constant diameter is fitted to the tank.

The water level is shown as a function of time in the graph on the right. The diameter of the tank is 20.0 cm. The length of the pipe is 1.010 m, its radius is 8.3 mm. The density of water is equal to 1000 kg/m^3. Data in Single_Tank_Water.xls.

a. Consider the system dynamics model diagram of the draining of a single tank in the following figure. Explain the model in words.
b. Write the expressions for delta_p and IV. V: volume, IV: volume current, k: turbulent flow factor, b: exponent in power law, A: tank cross section, h: water level, delta_p: pressure difference, p_a: ambient pressure.
c. Use the comparison of data and model to determine the flow factor in the simplified turbulent flow law
I_V = k·SQRT(delta_pR)
d. Demonstrate by combining the appropriate expressions that if we use the above flow law, the Bernoulli effect is included in the flow factor k. If we correct for this effect, what is the effective flow factor?
e. Calculate the Reynolds number for a few points. Should the flow be turbulent?



Click to obtain graph as pdf.