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By Dan Helgerson, Technical Editor, Fluid Power Journal
My daughter and son-in-law are very athletic and have 4 highly active boys. Recently, they had to replace their electric water heater. They hoped to have a system that supplied more hot water to feed the demands of the showers and washing machine. The plumber suggested they increase the temperature setting of the water heater to increase the supply of hot water. This suggestion struck me as kind of strange. How would hotter water at the source provide more hot water for the shower?
Words hold certain meanings and, sometimes, what we call something changes how we think about it. I don’t know about you, but I think of a water heater as just that. But the fact is, it is an energy storage device. It takes water at some ambient temperature and adds energy in the form of heat. This increases the energy density of the water. The water from the cold-water faucet has a very low energy density, while the water in the hot water tank has a relatively high energy density.
Most modern shower heads have a flow-limiting function to reduce the amount of water used. If the temperature setting (energy density) of the water heater is just right for a shower, then the duration of the shower would be limited to the volume of water in the heater. However, if the energy density setting of the water heater is much greater than would be comfortable in the shower, some low energy density (cold) water is added to lower the energy density at the shower head. However, the shower head will only allow a specific flow rate of water. By adding water with low energy density, less volume is taken from what is stored in the water heater.
The plumber was right! Because there is a fixed maximum flow rate at the shower head, adding water with low energy density reduces the energy density at the shower head and draws less from the stored energy in the water heater. The addition of cold water transforms the high energy density at the heater to the lower energy density required at the shower head. The rate at which energy is taken from the water heater is the same when the heater setting is perfect for the shower, as well as when the heater setting is way too hot.
OK, wait a second! Am I saying that the flow rate of water from the heater is the same in both instances? No! The flow of energy is the same. Energy is the combination of temperature and flow. The high-temperature/low-flow from the heater was converted to low-temperature/high-flow at the shower head. Energy density is a term that we use in describing the Variable Displacement Power Controller (VDPC).
Much like the high-temperature setting of the water heater, air compressors, receivers, hydraulic pumps, and accumulators all generate or store energy at a higher energy density than is required by the work being done. With fluid power, energy density is not produced by heat, but by pressure. While the shower adjusts the temperature (energy density) by adding cold water, the VDPC adjusts the pressure (energy density) by adding low-pressure fluid from the reservoir or the atmosphere. Only the amount of energy needed to do the work is drawn from the source. High-pressure/low-flow energy is taken from the source and then transformed to low-pressure/high-flow at the actuator.
In my first iteration of this article, I jumped right into the math. I determined the best water temperature and average flow rate for showers. I plugged in my equations for units of energy (UE) and units of power (UP). I used both metric and Imperial units. I made a spreadsheet with all the data. It was great! However, the whole point was to have a simple example to help explain the workings of the VDPC. When I reread what I had written, I realized that only a certain subset of readers would bother to read it. Since I didn’t want all that valuable information to go to waste, I am including it below.
Original Setting
New Setting
Metric
US
Metric
US
Tank Size | l (gal)
150
40
150
40
Temp | °C (°F)
38
100
60
159
UE | l/°C (gal/°F)
5,700
3,978
9,000
6,282
Shower | liter (gallons)
7.5
2
7.5
2
From Tank | liter (gallon)
7.5
2
4.8
1.3
UP | lpm/°C (gpm/°F)
285
199
285
199
From Cold | liter (gallon)
0.0
0.0
2.8
0.7
Time | minutes
20
20
32
32
Breaking It Down
A typical shower head uses about 7.5 lpm at 38 °C (2 gpm at 100 °F). Converting this to units of power (UP), we have 7.5 lpm × 38 °C = 285 lpm/°C (2 gpm × 100 °F = 200 gpm/°F) UP. A 150-liter (40-gallon) water heater, set at 38 °C (100 °F) has 5,700 liters/°C (4,000 gallons/°F) of stored UE. Using 285 lpm/°C (200 gpm/°F) would drain the tank of hot water in 20 minutes.
The same water heater set at 60 °C (159 °F) would have 150 liters × 60 °C = 9,000 UE (40 gallons × 159 °F = 6,341 UE). The tank would hold the same amount of water, but the energy density (heat/unit) would be much greater. However, there is too much energy in the water to be safely used. It is way too hot!
Bear with me now. The amount of energy I need at the shower head is 285 liters/°C (200 gallons/°F) The shower head will only take 7.5 lpm (2 gpm). By adjusting the faucet so that 2.8 lpm (.7 gpm) of cold water (near zero energy density) is added to the shower head, only 4.8 lpm (1.3 gpm) are drawn from the water heater. The power density at the shower head is 4.8 lpm × 60 °C = 285 lpm/°C (0.7 gpm × 159 °F = 200).
Maintaining the correct energy density at the shower head by augmenting the flow from the water heater with cold (near zero energy density) water increases the duration of hot water flow from 20 minutes to 32 minutes.
One of the functions of the VDPC is to reconfigure the energy density of the fluid to match the energy requirement of the actuator. However, in this case, the energy density is due to pressure, not temperature. The VDPC, in the pressure-reducing mode, takes only the units of energy (UE) from the source that are required by the actuator. It then draws a volume of near-zero energy units from the reservoir to provide the energy density needed by the actuator.
If you read this whole thing, I am proud of you.
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