Eat118 energy conversion - calculate the loss coefficients

Question

Coursework - Thermofluids

A water tank empties by gravity into another tank via an inclined pipe, as shown in Fig. 1 below. Both tanks are open to the atmosphere and the difference in levels is h. Since the tanks are large, h can be assumed to be constant.

Using the individual data assigned to you, calculate:
1. Secondary loss coefficients k_L2 and k_L3.
2. The length of the small diameter pipe, in meters.
3. The volumetric flow rate Q through the connecting pipes, in m³/s.
4. The water velocity in each pipe (V₁, V₂) and hence the corresponding Reynolds numbers (Re₁,Re₂).
5. The individual primary and secondary head losses, in meters (h_f1, h_f2, h_L1 to h_L4).

Fig. 1 Water tank system

Note that both bends have the same centreline radius (r = 300 mm) and both horizontal sections of the pipe of diameter d1 have the same length. You have been assigned a value of the secondary loss coefficient associated with the entry to the smaller pipe (k_L1). However, you are required to calculate the loss coefficients for the bends (k_L2) and the sudden expansion (k_L3), using the data assigned to you. The loss coefficient associated with entry to the second reservoir (k_L4) is 1. You will also be assigned values for the friction factor for each pipe, f₁ and f₂. Assume that the dynamic viscosity and density of water are 1.002×10^-3 Pa.s and 998 kg/m3, respectively.

Notes:
- You are assigned the following data: h, d₁, d₂, L₁, L₂ (all in metres); θ (degrees); loss coefficients k_L1, f₁, f₂.
- When you estimate the length of the small diameter pipe, you may ignore the effect of the bend radius (i.e. assume it is made of three straight sections). Radius r is given only to enable you to estimate the loss coefficient associated with the bends, using Fig. 2.
- This assignment contributes 25% to the overall module mark.

The loss coefficients associated with the pipe bends can be estimated from the graph shown in Fig. 2:

Fig. 2: Pipe bend loss coefficient

Submission requirements:

- Submit your report on Canvas in PDF format, on or before the deadline.
- The FIRST PAGE should be a summary table, in the format shown below. Enter your answers in the spaces provided.
- Subsequent pages will be your hand-written calculations. Keep them as neat as you can, as marks will be deducted for work that is illegible.