Question

Reconsider Prob. \(5-168 .\) Using EES (or other) software, investigate the effect of the inlet temperature of cold water on the energy saved by using the lowflow shower head. Let the inlet temperature vary from \(10^{\circ} \mathrm{C}\) to \(20^{\circ} \mathrm{C}\). Plot the electric energy savings against the water inlet temperature, and discuss the results.

Short answer

Answer: The inlet temperature of cold water affects the energy saved by using a lowflow showerhead by changing the energy required to heat the water for both the regular and lowflow showers. As the inlet temperature increases, the energy required for heating the water generally decreases, which leads to lower electric energy savings. A plot of electric energy savings against the water inlet temperature will show trends related to the relationship between the inlet temperature and energy savings, the rate at which energy savings change with the temperature, and any other relevant factors affecting energy conservation.

Step-by-step solution

Recall the given problem and the associated calculations

In Prob. 5-168, we analyzed the energy savings of using a lowflow showerhead. We calculated the electric energy savings by comparing the energy needed to heat the water with a regular showerhead and the energy needed to heat the water with a lowflow showerhead. To do so, we needed to compute the mass flow rates and temperature differences for both types of showerheads.

Set up a table for the inlet temperatures and electric energy savings

We will set up a table with columns for the inlet temperature, energy saved using a lowflow showerhead, and energy saved using the regular showerhead. We will fill in this table with the calculated values for the various inlet temperatures. The resulting table will be used to create the plot.

Compute the electric energy savings for each inlet temperature

For each inlet temperature between 10°C and 20°C, we will calculate the electric energy savings as follows: 1. Determine the mass flow rate and temperature difference for both the lowflow showerhead and the regular showerhead (as done in Prob. 5-168). 2. Calculate the energy required to heat the water for both showers using the specific heat of water and the temperature difference. 3. Compute the electric energy savings by subtracting the energy needed for the lowflow showerhead from the energy needed for the regular showerhead. Remember to record the calculated values in the table created in Step 2.

Plot the electric energy savings against the water inlet temperature

After computing the electric energy savings for each inlet temperature, we will create a plot with the inlet temperature on the x-axis and the electric energy savings on the y-axis. This will clearly show the trend and the effect of temperature on energy savings.

Analyze the results and discuss trends

Once the plot is created, analyze the results and discuss any trends observed. This could include information on the relationship between the inlet temperature and energy savings, the rate at which energy savings change with the temperature, and any other interesting findings. The discussion should give a clear understanding of how the inlet temperature affects the energy saved by using the lowflow showerhead.