The relationship between flow rate and temperature difference

Investigation of Flow rate and temperature difference

Introduction

My coursework is based on the principle of how an electric shower works. The common assumption is that in order to alter the temperature i.e. increase or decrease it, there is a heating implement in place which does this, but my investigation has proven this is not the variable. There is a heating implement but the heat is kept constant. The temperature of the water coming out of the shower depends on the flow rate of the water.

This investigation also involves the concept of energy transfer. The conservation law of energy states that “energy can neither be created nor destroyed but can only be transferred from 1 body to another through a medium”. In this case the energy is being transferred is heat. The transfer is heat energy from the hot water in the metal container by the metal container ( medium - free electrons in metal ) to the water flowing through the pipe.

I am investigating the effect of a changing flow rate on the temperature difference in a pipe. It will be important for me to carry out my experiment precisely and get a reasonable set of results because of all the variables involved such as temperature, and for the flow resistance in the pipe - viscosity, density, friction with pipe, specific heat capacity e.t.c.

Factors affecting my investigation

Viscosity

The resistance to flow in a liquid can be characterised in terms of the viscosity of the fluid if the flow is smooth. Viscosity is a measure of the resistance of a to deform under . It is commonly perceived as "thickness", or resistance to pouring. Viscosity describes a 's internal resistance to flow and may be thought of as a measure of fluid . Thus, is "thin", having a lower viscosity, while is "thick" having a higher viscosity. All real fluids (except ) have some resistance to shear stress, but a fluid which has no resistance to shear stress is known as an ideal fluid. Viscosities of all liquids are strongly temperature dependent, increasing for gases and decreasing for liquids as the temperature increases.

The of dynamic viscosity (Greek symbol: μ) is the - (Pa·s), which is identical to 1 ·m−1·s−1.It has been found that the relationship between viscosity and the flow rate of a liquid is directly proportional.

With most liquid flow measurement instruments, the flow rate is determined inferentially by measuring the liquid's velocity or the change in kinetic energy. Velocity depends on the pressure differential that is forcing the liquid through a pipe because the pipe's cross-sectional area is known and remains constant, the average velocity is an indication of the flow rate. The basic relationship for determining the liquid's flow rate in such cases is:

Q = V x A

where

Q = liquid flow through the pipe

V = average velocity of the flow

A = cross-sectional area of the pipe

Specific heat capacity (SHC)

The specific heat is the amount of per unit mass required to raise the of 1 gram of a substance by one degree Celsius. The relationship between heat and temperature change is usually expressed in the form shown below where c is the specific heat.

Q = m c ΔT

Q = heat energy put into or taken out of the substance

m = mass of the substance

c = specific heat capacity

The SI units for measuring specific heat capacity are either joules per gram per kelvin (J g–1 K–1) or joules per mole per kelvin (J mol–1 K–1)