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Air flows through a 10 cm internal diameter tube at the rate of 75 kg/hr. Measurements indicate that at a particular point in the tube, the pressure and temperature of air are 1.5 bar and 325 K whilst the tube wall temperature is 375 K. Find heat transfer rate from one meter length in the region of this point
The general non-dimensional correlation for turbulent flow in the tube is
Nu = 0.023 (Re) 0.8 (Pr) 0.4
Where the fluid properties are evaluated at the bulk temperature
The general non-dimensional correlation for turbulent flow in the tube is
Nu = 0.023 (Re) 0.8 (Pr) 0.4
Where the fluid properties are evaluated at the bulk temperature
- a)147.35 W
- b)157.35 W
- c)167.35 W
- d)177.35 W
Correct answer is option 'D'. Can you explain this answer?
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Air flows through a 10 cm internal diameter tube at the rate of 75 kg/...
Q = h A d t, where h = (Nu) (k)/l = 177.35 W.
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Air flows through a 10 cm internal diameter tube at the rate of 75 kg/...
Given data:
Diameter of the tube (D) = 10 cm
Mass flow rate (m) = 75 kg/hr
Pressure (P) = 1.5 bar
Temperature of fluid (Tf) = 325 K
Wall temperature (Tw) = 375 K
We need to find the heat transfer rate from one meter length in the region of this point.
Formula used:
The heat transfer rate can be calculated using the following formula:
q = h * A * (Tw - Tf)
where q is the heat transfer rate, h is the heat transfer coefficient, A is the surface area of the tube and (Tw - Tf) is the temperature difference between the wall and the fluid.
Heat transfer coefficient (h) can be calculated using the Nusselt number (Nu) and the thermal conductivity of the fluid (k) as follows:
h = (Nu * k) / D
Nusselt number (Nu) can be calculated using the following correlation:
Nu = 0.023 * Re^0.8 * Pr^0.4
where Re is the Reynolds number and Pr is the Prandtl number.
Reynolds number (Re) can be calculated as:
Re = (m / (pi * D * v))
where v is the kinematic viscosity of the fluid.
Prandtl number (Pr) can be calculated as:
Pr = (Cp * mu) / k
where Cp is the specific heat at constant pressure, mu is the dynamic viscosity of the fluid and k is the thermal conductivity of the fluid.
Solution:
We can start by finding the fluid properties at the bulk temperature. Assuming the bulk temperature is the average of the wall and fluid temperatures, we get:
Tb = (Tw + Tf) / 2 = (375 + 325) / 2 = 350 K
Using the ideal gas law, we can calculate the density of the fluid at the bulk temperature:
P = rho * R * Tb
where R is the gas constant and rho is the density of the fluid.
rho = P / (R * Tb) = (1.5 * 10^5) / (287 * 350) = 12.92 kg/m^3
Using the Sutherland's formula, we can calculate the kinematic viscosity of the fluid at the bulk temperature:
v = (C * Tb^(3/2)) / (Tb + S)
where C and S are constants that depend on the fluid.
For air, C = 1.458 * 10^-6 kg / (m*s*(K^0.5)) and S = 110.4 K.
v = (1.458 * 10^-6 * 350^(3/2)) / (350 + 110.4) = 1.36 * 10^-5 m^2/s
Using the specific heat at constant pressure and dynamic viscosity of air, we can calculate the Prandtl number:
Cp = 1005 J/kg*K
mu = 1.79 * 10^-5 kg/(m*s)
Pr = (Cp * mu) / k
where k is the thermal conductivity of air.
For air, k = 0.0262 W/(m*K)
Pr = (1005 * 1.79 * 10^-5) / 0.0262 = 0.685
Diameter of the tube (D) = 10 cm
Mass flow rate (m) = 75 kg/hr
Pressure (P) = 1.5 bar
Temperature of fluid (Tf) = 325 K
Wall temperature (Tw) = 375 K
We need to find the heat transfer rate from one meter length in the region of this point.
Formula used:
The heat transfer rate can be calculated using the following formula:
q = h * A * (Tw - Tf)
where q is the heat transfer rate, h is the heat transfer coefficient, A is the surface area of the tube and (Tw - Tf) is the temperature difference between the wall and the fluid.
Heat transfer coefficient (h) can be calculated using the Nusselt number (Nu) and the thermal conductivity of the fluid (k) as follows:
h = (Nu * k) / D
Nusselt number (Nu) can be calculated using the following correlation:
Nu = 0.023 * Re^0.8 * Pr^0.4
where Re is the Reynolds number and Pr is the Prandtl number.
Reynolds number (Re) can be calculated as:
Re = (m / (pi * D * v))
where v is the kinematic viscosity of the fluid.
Prandtl number (Pr) can be calculated as:
Pr = (Cp * mu) / k
where Cp is the specific heat at constant pressure, mu is the dynamic viscosity of the fluid and k is the thermal conductivity of the fluid.
Solution:
We can start by finding the fluid properties at the bulk temperature. Assuming the bulk temperature is the average of the wall and fluid temperatures, we get:
Tb = (Tw + Tf) / 2 = (375 + 325) / 2 = 350 K
Using the ideal gas law, we can calculate the density of the fluid at the bulk temperature:
P = rho * R * Tb
where R is the gas constant and rho is the density of the fluid.
rho = P / (R * Tb) = (1.5 * 10^5) / (287 * 350) = 12.92 kg/m^3
Using the Sutherland's formula, we can calculate the kinematic viscosity of the fluid at the bulk temperature:
v = (C * Tb^(3/2)) / (Tb + S)
where C and S are constants that depend on the fluid.
For air, C = 1.458 * 10^-6 kg / (m*s*(K^0.5)) and S = 110.4 K.
v = (1.458 * 10^-6 * 350^(3/2)) / (350 + 110.4) = 1.36 * 10^-5 m^2/s
Using the specific heat at constant pressure and dynamic viscosity of air, we can calculate the Prandtl number:
Cp = 1005 J/kg*K
mu = 1.79 * 10^-5 kg/(m*s)
Pr = (Cp * mu) / k
where k is the thermal conductivity of air.
For air, k = 0.0262 W/(m*K)
Pr = (1005 * 1.79 * 10^-5) / 0.0262 = 0.685
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Air flows through a 10 cm internal diameter tube at the rate of 75 kg/hr. Measurements indicate that at a particular point in the tube, the pressure and temperature of air are 1.5 bar and 325 K whilst the tube wall temperature is 375 K. Find heat transfer rate from one meter length in the region of this pointThe general non-dimensional correlation for turbulent flow in the tube isNu = 0.023 (Re)0.8(Pr)0.4Where the fluid properties are evaluated at the bulk temperaturea)147.35 Wb)157.35 Wc)167.35 Wd)177.35 WCorrect answer is option 'D'. Can you explain this answer?
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Air flows through a 10 cm internal diameter tube at the rate of 75 kg/hr. Measurements indicate that at a particular point in the tube, the pressure and temperature of air are 1.5 bar and 325 K whilst the tube wall temperature is 375 K. Find heat transfer rate from one meter length in the region of this pointThe general non-dimensional correlation for turbulent flow in the tube isNu = 0.023 (Re)0.8(Pr)0.4Where the fluid properties are evaluated at the bulk temperaturea)147.35 Wb)157.35 Wc)167.35 Wd)177.35 WCorrect answer is option 'D'. Can you explain this answer? for Chemical Engineering 2024 is part of Chemical Engineering preparation. The Question and answers have been prepared according to the Chemical Engineering exam syllabus. Information about Air flows through a 10 cm internal diameter tube at the rate of 75 kg/hr. Measurements indicate that at a particular point in the tube, the pressure and temperature of air are 1.5 bar and 325 K whilst the tube wall temperature is 375 K. Find heat transfer rate from one meter length in the region of this pointThe general non-dimensional correlation for turbulent flow in the tube isNu = 0.023 (Re)0.8(Pr)0.4Where the fluid properties are evaluated at the bulk temperaturea)147.35 Wb)157.35 Wc)167.35 Wd)177.35 WCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Chemical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Air flows through a 10 cm internal diameter tube at the rate of 75 kg/hr. Measurements indicate that at a particular point in the tube, the pressure and temperature of air are 1.5 bar and 325 K whilst the tube wall temperature is 375 K. Find heat transfer rate from one meter length in the region of this pointThe general non-dimensional correlation for turbulent flow in the tube isNu = 0.023 (Re)0.8(Pr)0.4Where the fluid properties are evaluated at the bulk temperaturea)147.35 Wb)157.35 Wc)167.35 Wd)177.35 WCorrect answer is option 'D'. Can you explain this answer?.
Air flows through a 10 cm internal diameter tube at the rate of 75 kg/hr. Measurements indicate that at a particular point in the tube, the pressure and temperature of air are 1.5 bar and 325 K whilst the tube wall temperature is 375 K. Find heat transfer rate from one meter length in the region of this pointThe general non-dimensional correlation for turbulent flow in the tube isNu = 0.023 (Re)0.8(Pr)0.4Where the fluid properties are evaluated at the bulk temperaturea)147.35 Wb)157.35 Wc)167.35 Wd)177.35 WCorrect answer is option 'D'. Can you explain this answer? for Chemical Engineering 2024 is part of Chemical Engineering preparation. The Question and answers have been prepared according to the Chemical Engineering exam syllabus. Information about Air flows through a 10 cm internal diameter tube at the rate of 75 kg/hr. Measurements indicate that at a particular point in the tube, the pressure and temperature of air are 1.5 bar and 325 K whilst the tube wall temperature is 375 K. Find heat transfer rate from one meter length in the region of this pointThe general non-dimensional correlation for turbulent flow in the tube isNu = 0.023 (Re)0.8(Pr)0.4Where the fluid properties are evaluated at the bulk temperaturea)147.35 Wb)157.35 Wc)167.35 Wd)177.35 WCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Chemical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Air flows through a 10 cm internal diameter tube at the rate of 75 kg/hr. Measurements indicate that at a particular point in the tube, the pressure and temperature of air are 1.5 bar and 325 K whilst the tube wall temperature is 375 K. Find heat transfer rate from one meter length in the region of this pointThe general non-dimensional correlation for turbulent flow in the tube isNu = 0.023 (Re)0.8(Pr)0.4Where the fluid properties are evaluated at the bulk temperaturea)147.35 Wb)157.35 Wc)167.35 Wd)177.35 WCorrect answer is option 'D'. Can you explain this answer?.
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