Fluid Mechanics: Fundamentals and Applications
4th Edition
ISBN: 9781259696534
Author: Yunus A. Cengel Dr., John M. Cimbala
Publisher: McGraw-Hill Education
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Chapter 12, Problem 88P
To determine
Velocity, static temperature and static pressure at the duct inlet.
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Helium is heated as it flows subsonically through a 10 cm × 10 cm square duct. The properties of helium at the inlet are maintained at Ma1 = 0.6, P1 = 350 kPa, and T1 = 420 K at all times. Disregarding frictional losses, determine the highest rate of heat transfer to the air in the duct without affecting the inlet conditions.
Air is heated as it flows subsonically through a 5 cm × 10 cm duct. The properties of air at the inlet are maintained at Ma1 = 0.6, P1 = 350 kPa, and T1 = 420 K at all times. Disregarding frictional losses, determine the highest rate of heat transfer to the air in the duct without affecting the inlet conditions. Take the properties of air to be k = 1.4, cp = 1.005 kJ/kg·K, and R = 0.287 kJ/kg·K.
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Chapter 12 Solutions
Fluid Mechanics: Fundamentals and Applications
Ch. 12 - What is dynamic temperature?Ch. 12 - Calculate the stagnation temperature and pressure...Ch. 12 - Prob. 6PCh. 12 - Prob. 7PCh. 12 - Prob. 8EPCh. 12 - Prob. 9PCh. 12 - Products of combustion enter a gas turbine with a...Ch. 12 - Is it possible to accelerate a gas to a supersonic...Ch. 12 - Prob. 72EPCh. 12 - Prob. 73P
Ch. 12 - Prob. 74PCh. 12 - Prob. 75PCh. 12 - For an ideal gas flowing through a normal shock,...Ch. 12 - Prob. 77CPCh. 12 - On a T-s diagram of Raleigh flow, what do the...Ch. 12 - What is the effect of heat gain and heat toss on...Ch. 12 - Prob. 80CPCh. 12 - Prob. 81CPCh. 12 - Prob. 82CPCh. 12 - Argon gas enters a constant cross-sectional area...Ch. 12 - Prob. 84EPCh. 12 - Prob. 85PCh. 12 - Prob. 86PCh. 12 - Prob. 87EPCh. 12 - Prob. 88PCh. 12 - Prob. 89PCh. 12 - Prob. 90PCh. 12 - Prob. 91PCh. 12 - Prob. 93CPCh. 12 - Prob. 94CPCh. 12 - Prob. 95CPCh. 12 - Prob. 96CPCh. 12 - Prob. 97CPCh. 12 - Prob. 98CPCh. 12 - Prob. 99CPCh. 12 - Prob. 100CPCh. 12 - Prob. 101PCh. 12 - Air enters a 5-cm-diameter, 4-m-long adiabatic...Ch. 12 - Helium gas with k=1.667 enters a 6-in-diameter...Ch. 12 - Air enters a 12-cm-diameter adiabatic duct at...Ch. 12 - Prob. 105PCh. 12 - Air flows through a 6-in-diameter, 50-ft-long...Ch. 12 - Air in a room at T0=300k and P0=100kPa is drawn...Ch. 12 - Prob. 110PCh. 12 - Prob. 112PCh. 12 - Prob. 113PCh. 12 - Prob. 114PCh. 12 - Prob. 115PCh. 12 - Prob. 116EPCh. 12 - A subsonic airplane is flying at a 5000-m altitude...Ch. 12 - Prob. 118PCh. 12 - Prob. 119PCh. 12 - Prob. 120PCh. 12 - Prob. 121PCh. 12 - Prob. 122PCh. 12 - Prob. 123PCh. 12 - An aircraft flies with a Mach number Ma1=0.9 at an...Ch. 12 - Prob. 125PCh. 12 - Helium expands in a nozzle from 220 psia, 740 R,...Ch. 12 - Prob. 127PCh. 12 - Prob. 128PCh. 12 - Prob. 129PCh. 12 - Prob. 130PCh. 12 - Prob. 131PCh. 12 - Prob. 132PCh. 12 - Prob. 133PCh. 12 - Prob. 134PCh. 12 - Prob. 135PCh. 12 - Prob. 136PCh. 12 - Prob. 137PCh. 12 - Prob. 138PCh. 12 - Air is cooled as it flows through a 30-cm-diameter...Ch. 12 - Prob. 140PCh. 12 - Prob. 141PCh. 12 - Prob. 142PCh. 12 - Prob. 145PCh. 12 - Prob. 148PCh. 12 - Prob. 149PCh. 12 - Prob. 150PCh. 12 - Prob. 151PCh. 12 - Prob. 153PCh. 12 - Prob. 154PCh. 12 - Prob. 155PCh. 12 - Prob. 156PCh. 12 - Prob. 157PCh. 12 - Prob. 158PCh. 12 - Prob. 159PCh. 12 - Prob. 160PCh. 12 - Prob. 161PCh. 12 - Prob. 162PCh. 12 - Assuming you have a thermometer and a device to...
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- Air flows through a device such that the stagnation pressure is 0.4 MPa, the stagnation temperature is 400°C, and the velocity is 520 m/s. Determine the static pressure and temperature of the air at this statearrow_forwardAir flows with negligible friction through a 6-in-diameter duct at a rate of 9 lbm/s. The temperature and pressure at the inlet are T1 = 800 R and P1 = 30 psia, and the Mach number at the exit is Ma2 = 1. Determine the rate of heat transfer and the pressure drop for this section of the duct.arrow_forwardConsider subsonic Fanno flow accelerated to sonic velocity (Ma = 1) at the duct exit as a result of frictional effects. If the duct length is increased further, will the flow at the duct exit be supersonic, subsonic, or remain sonic? Will the mass flow rate of the fluid increase, decrease, or remain constant as a result of increasing the duct length?arrow_forward
- (b) Air flows through a cylindrical duct at a rate of 2.3 kg/s. Friction between air and the duct and friction within air can be neglected. The diameter of the duct is 10cm and the air temperature and pressure at the inlet are T₁ 450 K and P₁ = 200 kPa. If the Mach number at the exit is Ma2 determine the rate of heat transfer and the pressure difference across the duct. The constant pressure specific heat of air is cp = 1.005 kJ/kg-K. The gas constant of air is R = 0.287 kJ/kg-K and assume k = 1.4. -arrow_forwardIn air-conditioning applications, the temperature of air is measured by inserting a probe into the flow stream. Thus, the probe actually measures the stagnation temperature. Does this cause any significant error?arrow_forwardIs it possible to accelerate a fluid to supersonic velocities with a velocity other than the sonic velocity at the throat? Explainarrow_forward
- Consider supersonic Fanno flow that is decelerated to sonic velocity (Ma = 1) at the duct exit as a result of frictional effects. If the duct length is increased further, will the flow at the duct exit be supersonic, subsonic, or remain sonic? Will the mass flow rate of the fluid increase, decrease, or remain constant as a result of increasing the duct length?arrow_forwardCompressed air from the compressor of a gas turbine enters the combustion chamber at T1 = 700 K, P1 = 560 kPa, and Ma1 = 0.2 at a rate of 0.3 kg/s. Via combustion, heat is transferred to the air at a rate of 300 kJ/s as it flows through the duct with negligible friction. Determine the Mach number at the duct exit and the drop in stagnation pressure P01 – P02 during this process. Take the properties of air to be k = 1.4, cp = 1.005 kJ/kg·K, and R = 0.287 kJ/kg·K. The Mach number at the duct exit is____ . The drop in stagnation pressure is____ kPa.arrow_forwardCarbon dioxide flows steadily through a varying cross- sectional-area duct such as a nozzle at a mass flow rate of 3 kg/s. The carbon dioxide enters the duct at a pressure of 1400 kPa and 200°C with a low velocity, and it expands in the nozzle to a pressure of 200 kPa. The duct is designed so that the flow can be approximated as isentropic. Determine the following parameters at each location along the duct that corresponds to a pressure drop of 200 kPa: (i) density; (ii) velocity: (iii) flow area; (iv) mach number. You may assume: • Carbon dioxide is an ideal gas with constant specific heats at room temperature; • Flow through the duct is steady, one-dimensional and isentropic. Use c, 0 846 kJ/kgk andk = 1.289 throughout the calculations, which are the constant-pressure specific heat and specific heat ratio values of carbon dioxide at room temperature. The gas constant of carbon dioxide is R = 0.1889 kJ/kg K.arrow_forward
- Air enters a compressor with a stagnation pressure of 100 kPa and a stagnation temperature of 35°C, and it is compressed to a stagnation pressure of 900 kPa. Assuming the compression process to be isentropic, determine the power input to the compressor for a mass flow rate of 0.04 kg/sarrow_forwardAir in an automobile tire is maintained at a pressure of 220 kPa (gage) in an environment where the atmospheric pressure is 94 kPa. The air in the tire is at the ambient temperature of 25°C. A 4-mm-diameter leak develops in the tire as a result of an accident. Approximating the flow as isentropic determine the initial mass flow rate of air through the leak.arrow_forwardAir flows steadily through a varying cross-sectional area duct such as a nozzle at a mass flow rate of 10 lb/s. The air enters the duct at a pressure of 200 lb/in2 and 445°F with a low velocity, and it expands in the nozzle to an exit pressure of 30 lb/in2. The duct is designed so that the flow can be approximated as isentropic. Determine the density, velocity, flow area, and Mach number at each location along the duct that corresponds to an overall pressure drop of 30 lb/in2.arrow_forward
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