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## Blog Posts (14)

• Volumetric Flow Rate - 5W1H

What is volumetric flow rate? The volumetric flow rate is volume displaced per unit time and it is expressed as Why use volumetric flow rate? It is a measure of the quantity of the fluid that is being displaced from one place to other. This is an important parameter when designing pumps, compressors, turbines, piping systems, heat exchangers, etc What are the units of volumetric flow rate? In the metric system of units, In the metric/english system of units, What is the difference between mass flow rate and volume flow rate? The mass flow rate is nothing but a multiplication of volume flow rate with the density of the fluid. It is expressed in kg/s in metric units. Why volumetric flow rate is not a conserved quantity? If the fluid is compressible then the volume flow rate may change from place to place with respect to temperature and pressure (in the case of compressors) and it may not be conserved as the density may vary. The mass flow rate is always(and must) a conserved quantity but the volume flow rate is not. How to calculate volume flow rate? or

• Throttling Process

The expansion of the fluid in the expansion valve/turbines results in a pressure drop in the thermal systems which produces thermodynamic work. Sometimes there is a need to reduce the fluid pressure without producing any thermodynamic work. This pressure drop is obtained by using throttling valves, which result in the pressure drop and do not produce any thermodynamic work. What is the throttling process? Throttling is a process of reducing the pressure of the fluid significantly by passing it through flow-restricting devices. Which devices are used in throttling? An Orifice, capillary tube, porous plugs, etc Does the throttling process produce any thermodynamic work? No. Throttling does not produce any thermodynamic work. Which property remains constant during the throttling process? Enthalpy. That is why the throttling process is called an isenthalpic process. Why does enthalpy remain constant during the isenthalpic process? Let's apply the energy balance equation between the upstream and downstream of the throttling valve. Q + h1= W + h2 + d(KE) + d(PE) Q = 0 Reason: There is not enough time and surface area available for heat transfer W = 0 Reason: There is no lifting of any weight (no thermodynamic work) d(PE) = 0 Reason: There is no potential head difference d(KE) =~ 0 Reason: there may be an increase in velocity at the outlet compared to the inlet but in many cases the change in kinetic energy is insignificant. Hence we remain with h1=~h2 (kJ/Kg) i.e. u1 + P1v1 = u2 + P2v2 internal energy + flow work = constant What happens to temperature in the throttling process? Does internal energy change in throttling? For throttling processes, internal energy + flow work = constant If we talk in terms of internal energy and flow work, If flow energy increases during the process it causes the internal energy to decrease. Temperature is directly dependent on internal energy hence in this case the temperature reduces. On the other hand, if the flow energy reduces downstream (the work required to push fluid is less at the outlet) and internal energy rises the temperature of the fluid increases. The magnitude of rise or drop in temperature is decided by the Joule-Thomson coefficient. What is Joule-Thomson coefficient? It is a measure of the rate of change of temperature with respect to pressure during a constant enthalpy process. Remember that in the throttling process the pressure always drops. So, the denominator is always negative in the equation. Hence, if the temperature of the fluid drops the Joule-Thomson coefficient is positive. Conversely, if the temperature of the fluid increases Joule-Thomson coefficient is negative. Now, let's understand T-P plot with a single constant enthalpy line as shown below. This constant enthalpy line is drawn by doing experiments using different sizes of porous plugs and different initial pressure and temperature conditions. The outlet pressure and temperature are plotted for each inlet condition of temperature and pressure with different sizes of porous plugs. Each constant enthalpy line on the T-P plot has one zero slope point (where the Joule-Thomson coefficient is zero). What is the inversion line? The locus of all the points at which the Joule-Thomson coefficient is zero is called the inversion line or inversion curve. What is inversion temperature? The temperature at a point where the constant enthalpy line intersects the inversion line is called inversion temperature. What is the maximum inversion temperature? The point at which the inversion curve intersects the y axis (zero pressure line) is the maximum inversion temperature. If we look closely the slope of isenthalpic lines is negative to the right of the inversion curve which is nothing but the heating region and the slope is positive to the right of the inversion curve which is the cooling region. So, if the throttling is done in the heating region the temperature of the fluid increases whereas, the temperature drops if the throttling starts to the left of the inversion curve. If the cooling effect is needed after throttling then the initial temperature of the fluid must be below the maximum inversion temperature. For almost all the fluids this holds true naturally because their maximum inversion temperature is above room temperature. The only exceptions are Helium and Hydrogen where the maximum inversion temperatures are very low. Hence if we throttle hydrogen or helium at room temperatures they heat up even after throttling. Does the throttling valve increase velocity? Generally, the velocity at the downstream of throttling valve is more than the inlet velocity but the effect of change in velocity(KE) is insignificant in the energy balance equation. What is constant in the throttling process? Is the throttling process an adiabatic process? Enthalpy is constant in the throttling process that is why it is called the isenthalpic process. The heat transfer is negligible in the throttling process because it happens in a very short period of time as well as the surface area available for heat transfer is low. But capillary tubes can be the exception to this because they provide a higher surface area for heat transfer. Why throttling process is highly irreversible? The flow accelerates through a small passage but the flow then separates at the downstream of throttling valve. The high-speed fluid mixes with the low-speed fluid and all that shearing and roiling is what causes the dissipation. Friction is the number one reason for all the thermodynamic irreversibilities. Why temperature does not drop when ideal gas is throttled? Enthalpy of an ideal gas is a function of temperature only. h=h(T), which requires that temperature remains constant when the enthalpy remains constant. Therefore, the throttling process can not be used to lower the temperature of an ideal gas. What is the application of the throttling process in thermal systems? The throttling process is used in the vapor compression refrigeration systems because they reduce the pressure of the high-pressure refrigerant liquid which came out of the condenser to lower pressure. This causes a significant drop in the temperature of the refrigerant. This low-temperature refrigerant liquid-vapor mixture is then used to absorb heat from the refrigeration space. The advantage of using a throttling valve is that it does not produce any thermodynamic work and throttling valves are very cost-effective compared to expansion devices such as turbines. Hence, they cause a significant reduction in the initial cost of VCRS.

• Path Function vs Point Function

We come across a lot of properties and functions in Thermodynamics. These are divided mainly into path functions and point functions. All the Thermodynamic properties like volume, temperature, pressure, etc are point functions. Whereas the path functions are not properties of the system and are boundary phenomena. Path functions are path-dependent and are inexact differentials. Let's find out what these terms mean one by one. What is a boundary phenomenon? The quantities like heat and work are transferred between the system and the surroundings at the boundary during the interaction, in other words, the amount of heat and work transferred depends on the kind of process the system follows. But in the case of the state functions or point functions like volume, pressure, temperature, entropy, etc the change in the amount of these quantities is fixed between two states no matter what kind of processes they follow. The system does not possess the quantities which are boundary phenomena. On the other hand, properties like internal energy, temperature, pressure, etc are possessed by the system. What is an exact differential and what is an inexact differential? The exact differentials are functions whose integration is nothing but the difference between values at the endpoints or limits. For example, when the volume is integrated between two states V1 and V2, it equals the difference between V2 and V1. But, in the case of the inexact differentials, the integration or differentiation is not straightforward subtraction between endpoints. For example, work transfer is a path function hence an inexact differential. Its integral over a process can not be a simple difference between values at the endpoints. Rather, Also, I would like to mention here about the cyclic integral of the Thermodynamic properties. The properties are point functions and exact differentials hence when the cyclic integral is taken over the thermodynamic cycle the system goes back to the initial state hence the cyclic integral of the Thermodynamics properties is zero. Path function: Analogy with vectors Path function is a directional phenomenon that requires magnitude as well as direction for its complete description. They are analogous to vector quantities in some sense. A point function is analogous to a scalar quantity which only requires endpoint values for a complete description. Why do the heat and work are path functions? The heat and work can not be defined at a particular state point. They are always defined as quantities in transit (boundary phenomenon). The amount of heat transfer or work transfer does depend on how the process happens. Heat and work are not intrinsic properties of the system. Example 1: Suppose you want to go to the 10th floor of the building and you have two options for reaching there, either you take a lift or you take the stairs. The amount of work done by your body during this process is completely different in each case. If you take a lift your body needs to do a small amount of effort on the other hand if you take a staircase route, your body will do so much work that it will get exhausted by the time you reach the 10th floor. Let's understand these concepts in a little more technical sense by using P-v and T-s diagrams. Example 2: Suppose you have already decided on initial and final state points and you are trying to find out the best suitable path to reach the final state point from the initial state point. There are multiple possibilities through which this can happen. I have shown 3 possible paths through which the system can change from initial state point 1 to final state point 2. We know that the areas under the curve in P-v and T-s diagrams represent Work and Heat respectively. As you can see from the following figure, in each case the area under the curve is different, that is the work done is different. This can also be proved using equations by adding up the work done in each process of the path. Similarly, The heat transferred in each case is also different. Hence it is safe to say that heat and work are path functions and they depend on the path followed. On the other hand, quantities like pressure, temperature, and volume are independent of the path. The pressure and volume values at state 2 are always exactly the same in all 3 cases above. What is the difference between path function and point function? Can you make a path function change to the point function? No, it can not be done. What can you do with all this information? What is the significance of path function and point function? It becomes easier when analyzing systems to choose the quantities that do not depend on the path.

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