Explanation Consider the air flows at steady state through one inlet and one exit system (pipe and duct flow). Hence, the inlet and exit mass flow rates are equal. m ˙ 1 = m ˙ 2 = m ˙ Write the energy rate balance equation for one inlet and one outlet system. [ Q ˙ 1 + W ˙ 1 + m ˙ ( h 1 + V 1 2 2 + g z 1 ) ] − [ Q ˙ 2 + W ˙ 2 + m ˙ ( h 2 + V 2 2 2 + g z 2 ) ] = Δ E ˙ system (I) Here, the rate of heat transfer is Q ˙ , the rate of work transfer is W ˙ , the enthalpy is h and the velocity is V , the gravitational acceleration is g , the elevation from the datum is z and the rate of change in net energy of the system is Δ E ˙ system ; the suffixes 1 and 2 indicates the inlet and outlet of the system. The air flows at steady state through the system. Hence, the rate of change in net energy of the system becomes zero. Δ E ˙ system = 0 The heat is added to the air by the electronic components of the computer. Neglect the heat transfer at the outlet, work transfer, kinetic and potential energies. The Equations (I) reduced as follows. [ 0 + Q ˙ 1 + m ˙ ( h 1 + 0 + 0 ) ] − [ 0 + 0 + m ˙ ( h 2 + 0 + 0 ) ] = 0 Q ˙ 1 + m ˙ h 1 − m ˙ h 2 = 0 Q ˙ 1 = m ˙ h 2 − m ˙ h 1 Q ˙ 1 = m ˙ ( h 2 − h 1 ) (II) The change in enthalpy is expresses as follow. h 2 − h 1 = c p ( T 2 − T 1 ) Here, the specific heat is c p , the exit temperature is T 2 and the inlet temperature is T 1 . Substitute c p ( T 2 − T 1 ) for h 2 − h 1 in Equation (II). Q ˙ 1 = m ˙ [ c p ( T 2 − T 1 ) ] = m ˙ c p ( T 2 − T 1 ) (III) Rearrange the Equation (III) to obtain the mass flow rate ( m ˙ ) . m ˙ = Q ˙ 1 c p ( T 2 − T 1 ) (IV) Write the formula for volumetric flow rate of air ( V ˙ ) in terms of mass flow rate and density. V ˙ = m ˙ ρ = m ˙ R T P (V) Here, the volumetric flow rate of air is V ˙ , the pressure is P , the gas constant of air is R and the temperature is T . Write the formula for inlet volumetric flow rate ( V ˙ ) in terms of cross sectional area and velocity. V ˙ = A V (VI) Here, the cross-sectional area of the hose is A and the velocity of the air is V . Write the formula for cross-sectional area of the fan casing whose cross section is circle. A = π D 2 4 Here, the diameter of the fan casing is D . Substitute π D 2 4 for A in Equation (VI) and rearrange to obtain diameter of fan casing. V ˙ = ( π D 2 4 ) V D 2 = 4 V ˙ π V D = 4 V ˙ π V (VII) Refer Table A-1, “Molar mass, gas constant, and critical-point properties”. The gas constant ( R ) of air is 0.287 kPa .m 3 /kg ⋅ K . Refer Table A-2 (b), “Ideal-gas specific heats of various common gases”. Obtain the specific heat at constant pressure ( c p ) of air corresponding to the average temperature of 45 ° C + 60 ° C 2 = 52

9th Edition

ISBN: 9781259822674

Author: Yunus A. Cengel Dr., Michael A. Boles

Publisher: McGraw-Hill Education

See similar textbooks

Concept explainers

Work and Heat Transfer

It is generally related to thermal engineering which tells about the use, creation, conversion and transfer of heat energy between the systems. It is also considered that to transfer heat from one source to another, transfer of masses is also required. T…

Videos

Question

Chapter 5.5, Problem 99P

To determine

The flow rate of the fan that needs to be installed and the diameter of the casing of the fan.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 5.5, Problem 98P

Chapter 5.5, Problem 100P

Students have asked these similar questions

5-36 Steam enters a nozzle at 400°C and 800 kPa with a velocity of 10 m/s and leaves at 375°C and 400 kPa while losing heat at a rate of 25 kW. For an inlet area of 800 cm², determine the velocity and the volume flow rate of the steam at the nozzle exit. 400°C 800 kPa 10 m/s Steam 375°C 400 kPa

A variable-load piston-cylinder device contains air (cp = 1.005 kJ/kgK; cv = 0.718 kJ/kgK) at 500 kPa and T=18 oC. A paddle wheel equipped within the system and turned by an external electric motor until 65 kJ/kg of work has been transferred to the air. During this process the gas volume is quadrupled while maintaining the temperature constant by transferring heat to the gas. Determine (a) the final pressure, (b) the amount of required heat transfer (c) Show this process on a P-v diagram. Do not use Table A-17 while solving this problem

3 A 40-L electrical radiator containing heating oil is placed in a 50-m³ room. Both the room and the oil in the radiator are initially at 10°C. The radiator with a rating of 2.4 kW is now turned on. At the same time, heat is lost from the room at an average rate of 0.35 kJ/s. After some time, the average temperature is measured to be 20°C for the air in the room, and 50°C for the oil in the radiator. Taking the density and the specific heat of the oil to be 950 kg/m3 and 2.2 kJ/kg-°C, respectively, determine how long the heater is kept on. Assume the room is well sealed so that there are no air leaks. The gas constant of air is R = 0.287 kPa-m³/kg-K (Table A-1). Also, c = 0.718 kJ/kg-K for air at room temperature (Table A-2). Oil properties are given to be p = 950 kg/m³ and Cp = 2.2 kJ/kg.°C. 3 10°C Room Radiator The heater is kept on for Q min. 4

Chapter 5 Solutions

Thermodynamics: An Engineering Approach

Ch. 5.5 - Name four physical quantities that are conserved...Ch. 5.5 - Define mass and volume flow rates. How are they...Ch. 5.5 - Does the amount of mass entering a control volume...Ch. 5.5 - Consider a device with one inlet and one outlet....Ch. 5.5 - The ventilating fan of the bathroom of a building...Ch. 5.5 - Air enters a 16-cm-diameter pipe steadily at 200...Ch. 5.5 - A steam pipe is to transport 200 lbm/s of steam at...Ch. 5.5 - A garden hose attached with a nozzle is used to...Ch. 5.5 - A steady-flow compressor is used to compress...Ch. 5.5 - Air enters the 1-m2 inlet of an aircraft engine at...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

The flow rate of the fan that needs to be installed and the diameter of the casing of the fan.

Solution Summary: The author analyzes the flow rate of the fan that needs to be installed and the diameter of its casing. The inlet and exit mass flow rates are equal.

Concept explainers

Videos

The flow rate of the fan that needs to be installed and the diameter of the casing of the fan.

Want to see the full answer?

Chapter 5 Solutions