Saturated liquid water at 1000 kPa flows at 2 kg / s inside a 10 -cm-outer-diameter steel pipe,

step 1 saturated liquid water at a given state flows inside a steel pipe. Outside the pipe we have a fl

Saturated liquid water at 1000 kPa flows at 2 kg / s inside...

Saturated liquid water at $1000 \mathrm{kPa}$ flows at $2 \mathrm{kg} / \mathrm{s}$ inside a 10 -cm-outer-diameter steel pipe, and outside of the pipe is a flow of hot gases at $1000 \mathrm{K}$ with a convection coefficient of $h=150 \mathrm{W} / \mathrm{m}^{2} \mathrm{K}$ Neglect any $\Delta T$ in the steel and any inside convection $h,$ and find the length of pipe needed to bring the water to saturated vapor.

Key Concepts

Convective Heat Transfer

This concept involves the transfer of heat from a fluid (in this case, hot gases) to a solid surface (the outer wall of the pipe) without the need for direct contact. It is characterized by a convection coefficient, which quantifies the effectiveness of heat exchange per unit area per unit temperature difference. The heat transfer rate can be calculated using the product of the convection coefficient, the surface area, and the temperature difference between the gas and the pipe surface.

Latent Heat of Vaporization

Latent heat of vaporization is the energy required to change a substance from the liquid phase to the vapor phase without a change in temperature. In this context, it represents the amount of energy per unit mass needed to convert saturated liquid water into saturated vapor. This concept is critical because the entire heat input from the external source is used to overcome this energy barrier during the phase change.

Energy Balance

The energy balance principle is used to equate the rate at which heat is transferred into the system (through convection from the hot gas) to the rate at which energy is consumed in converting water from a liquid to a vapor. By setting these two rates equal, one can solve for the necessary conditions, such as the length of the pipe, that will ensure complete phase transition of the water.

Pipe Geometry and Heat Transfer Area

The geometry of the pipe, specifically its diameter and length, directly influences the available surface area for heat transfer. A larger or longer pipe provides more area for convection, thereby increasing the total heat transfer rate. In engineering calculations, determining the appropriate surface area is essential for ensuring that the system meets the required energy input for processes like vaporization.

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