You would like to use a pipe-based continuous flow hydroponic system. In this configuration, the roots of the strawberry plants are exposed to water that flows continuously through cylindrical pipes, driven by a pressure pump. The pipes are oriented horizontally so that the nutrient-containing water flows in the axial (x) direction. You are wondering whether this design is sufficient to support the needs of your strawberry plants. Your hydroponics system requires you to pay for the costs of the electricity used to heat the water that flows through the pipes. Strawberry plants grow best when their roots are exposed to water at a temperature of 25°C. The water that flows through the pipes is stored in a tank (inside height = 2 m), which sits on the ground outside of a greenhouse. In July, the average air temperature is Tair = 26°C, with heat transfer coefficient hair = 20 W/m2·K. The temperature of the ground underneath the water tank is Tground = 10°C. The heat capacity of water is Cpwater = 4 kJ/kg·K. The thermal conductivity of water is 0.6 W/m·K. The tank is made of polyethylene (2-mm-thick), with thermal conductivity of 0.4 W/m·K. a) Sketch the system, labeling all temperatures, dimensions, and proportionality constants. You may assume that the ground, water, and air are at steady state. b) Sketch the electrical analogy to this system, labeling all temperatures, resistances, and heat flows. c) On separate graphs, sketch the heat flux and temperature as a function of position (from the air to the ground beneath the tank). Make sure that your sketches reflect that the system is at steady-state and account for the relative magnitudes of the thermal conductivities and heat transfer coefficient. You don’t need to calculate anything for these graphs. d) Do you need to heat the water? [Hint: first, find the steady-state temperature profile in the tank as a function of y-position, T(y). Then, find the average temperature of the water in the tank.]
You would like to use a pipe-based continuous flow hydroponic system. In this configuration, the roots of the strawberry plants are exposed to water that flows continuously through cylindrical pipes, driven by a pressure pump. The pipes are oriented horizontally so that the nutrient-containing water flows in the axial (x) direction. You are wondering whether this design is sufficient to support the needs of your strawberry plants.
Your hydroponics system requires you to pay for the costs of the electricity used to heat the water that flows through the pipes. Strawberry plants grow best when their roots are exposed to water at a temperature of 25°C. The water that flows through the pipes is stored in a tank (inside height = 2 m), which sits on the ground outside of a greenhouse.
In July, the average air temperature is Tair = 26°C, with heat transfer coefficient hair = 20 W/m2·K. The temperature of the ground underneath the water tank is Tground = 10°C. The heat capacity of water is Cpwater = 4 kJ/kg·K. The thermal conductivity of water is 0.6 W/m·K. The tank is made of polyethylene (2-mm-thick), with thermal conductivity of 0.4 W/m·K.
a) Sketch the system, labeling all temperatures, dimensions, and proportionality constants. You may assume that the ground, water, and air are at steady state.
b) Sketch the electrical analogy to this system, labeling all temperatures, resistances, and heat flows.
c) On separate graphs, sketch the heat flux and temperature as a function of position (from the air to the ground beneath the tank). Make sure that your sketches reflect that the system is at steady-state and account for the relative magnitudes of the thermal conductivities and heat transfer coefficient. You don’t need to calculate anything for these graphs.
d) Do you need to heat the water? [Hint: first, find the steady-state temperature profile in the tank as a function of y-position, T(y). Then, find the average temperature of the water in the tank.]
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