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Consider a hydrodynamically and thermally fully-developed, steady fluid flow of 1 kg/s in a uniformly heated pipe with diameter of 0.1 m and length of 40 m. A constant heat flux of magnitude 15000 W/m2 is imposed on the outer surface of the pipe. The bulk-mean temperature of the fluid at the entrance to the pipe is 200oC . The Reynolds number (Re) of the flow is 85000, and the Prandtl number (Pr) of the fluid is 5. The thermal conductivity and the specific heat of the fluid are 0.08 W∙m-1∙K-1and 2600 J∙kg-1∙K-1, respectively. The correlation Nu = 0.023 Re0.8 Pr0.4 is applicable, where the Nusselt Number (Nu) is defined on the basis of the pipe diameter. The pipe surface temperature at the exit is ________ oC (round off to the nearest integer).
Correct answer is '321.267'. Can you explain this answer?
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Consider a hydrodynamically and thermally fully-developed, steady flui...
Given:
- Fluid flow rate: 1 kg/s
- Pipe diameter: 0.1 m
- Pipe length: 40 m
- Heat flux on outer surface of the pipe: 15000 W/m2
- Bulk-mean temperature at the entrance: 200°C
- Reynolds number (Re): 85000
- Prandtl number (Pr): 5
- Thermal conductivity of fluid: 0.08 Wm-1K-1
- Specific heat of fluid: 2600 Jkg-1K-1
- Correlation for Nusselt number (Nu): Nu = 0.023 Re0.8 Pr0.4
Approach:
To find the pipe surface temperature at the exit, we need to calculate the Nusselt number and then use it to determine the heat transfer coefficient. Finally, we can calculate the pipe surface temperature using the heat flux and heat transfer coefficient.
Calculation:
Step 1: Calculate Nusselt number (Nu)
Using the given correlation:
Nu = 0.023 Re0.8 Pr0.4
Nu = 0.023 * 850000.8 * 50.4
Nu ≈ 253.92
Step 2: Calculate heat transfer coefficient (h)
The heat transfer coefficient can be calculated using the Nusselt number and thermal conductivity of the fluid:
h = Nu * k / D
Where k is the thermal conductivity of the fluid and D is the pipe diameter.
h = 253.92 * 0.08 / 0.1
h ≈ 203.136 W/m2K
Step 3: Calculate heat transfer rate (Q)
The heat transfer rate can be calculated using the heat transfer coefficient and the temperature difference between the fluid and the pipe surface:
Q = h * A * ΔT
Where A is the surface area of the pipe and ΔT is the temperature difference.
A = π * D * L
ΔT = Tbulk - Tsurface
Tbulk = 200°C (given)
Tsurface = ?
Q = 15000 W/m2 * π * 0.1 * 40 * (200 - Tsurface)
Step 4: Calculate pipe surface temperature (Tsurface)
To find the pipe surface temperature, we need to solve the equation obtained in step 3 for Tsurface:
15000 * π * 0.1 * 40 * (200 - Tsurface) = 203.136 * π * 0.1 * 40 * (200 - Tsurface)
Simplifying and solving the equation, we get:
Tsurface ≈ 321.267°C
Therefore, the pipe surface temperature at the exit is approximately 321.267°C, rounded off to the nearest integer.
- Fluid flow rate: 1 kg/s
- Pipe diameter: 0.1 m
- Pipe length: 40 m
- Heat flux on outer surface of the pipe: 15000 W/m2
- Bulk-mean temperature at the entrance: 200°C
- Reynolds number (Re): 85000
- Prandtl number (Pr): 5
- Thermal conductivity of fluid: 0.08 Wm-1K-1
- Specific heat of fluid: 2600 Jkg-1K-1
- Correlation for Nusselt number (Nu): Nu = 0.023 Re0.8 Pr0.4
Approach:
To find the pipe surface temperature at the exit, we need to calculate the Nusselt number and then use it to determine the heat transfer coefficient. Finally, we can calculate the pipe surface temperature using the heat flux and heat transfer coefficient.
Calculation:
Step 1: Calculate Nusselt number (Nu)
Using the given correlation:
Nu = 0.023 Re0.8 Pr0.4
Nu = 0.023 * 850000.8 * 50.4
Nu ≈ 253.92
Step 2: Calculate heat transfer coefficient (h)
The heat transfer coefficient can be calculated using the Nusselt number and thermal conductivity of the fluid:
h = Nu * k / D
Where k is the thermal conductivity of the fluid and D is the pipe diameter.
h = 253.92 * 0.08 / 0.1
h ≈ 203.136 W/m2K
Step 3: Calculate heat transfer rate (Q)
The heat transfer rate can be calculated using the heat transfer coefficient and the temperature difference between the fluid and the pipe surface:
Q = h * A * ΔT
Where A is the surface area of the pipe and ΔT is the temperature difference.
A = π * D * L
ΔT = Tbulk - Tsurface
Tbulk = 200°C (given)
Tsurface = ?
Q = 15000 W/m2 * π * 0.1 * 40 * (200 - Tsurface)
Step 4: Calculate pipe surface temperature (Tsurface)
To find the pipe surface temperature, we need to solve the equation obtained in step 3 for Tsurface:
15000 * π * 0.1 * 40 * (200 - Tsurface) = 203.136 * π * 0.1 * 40 * (200 - Tsurface)
Simplifying and solving the equation, we get:
Tsurface ≈ 321.267°C
Therefore, the pipe surface temperature at the exit is approximately 321.267°C, rounded off to the nearest integer.
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Community Answer
Consider a hydrodynamically and thermally fully-developed, steady flui...
Entrance temp (Tb inlet) 2000 C
Reynold number (Re) 85000
Prandtl number (Pr) =
Thermal conductivity ( K ) = 0.08 Wm-1K- 1
Specific heat of the fluid (Cp) 2600 J.kg -1K-1
Heat flux (q ") = 15000 W/m2
Diameter of pipe (D) = 0.1m
Length of the pipe (L) = 40 m
Fluid flow of mass (m) = 1 kg/s
To get Tb exit
Nusselt number,
So,
h = 307.5678 W/m2 K
Now for TW wall temperature
By newton's law of cooling
15000 = 307.567(TW exit - 272.498)
Hence, the pipe surface temperature at the exit is 321.267oC.
Reynold number (Re) 85000
Prandtl number (Pr) =
Thermal conductivity ( K ) = 0.08 Wm-1K- 1
Specific heat of the fluid (Cp) 2600 J.kg -1K-1
Heat flux (q ") = 15000 W/m2
Diameter of pipe (D) = 0.1m
Length of the pipe (L) = 40 m
Fluid flow of mass (m) = 1 kg/s
To get Tb exit
Nusselt number,
So,
h = 307.5678 W/m2 K
Now for TW wall temperature
By newton's law of cooling
15000 = 307.567(TW exit - 272.498)
Hence, the pipe surface temperature at the exit is 321.267oC.
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Consider a hydrodynamically and thermally fully-developed, steady fluid flow of 1 kg/s in a uniformly heated pipe with diameter of 0.1 m and length of 40 m. A constant heat flux of magnitude 15000 W/m2 is imposed on the outer surface of the pipe. The bulk-mean temperature of the fluid at the entrance to the pipe is 200oC . The Reynolds number (Re) of the flow is 85000, and the Prandtl number (Pr) of the fluid is 5. The thermal conductivity and the specific heat of the fluid are 0.08 Wm-1K-1and 2600 Jkg-1K-1, respectively. The correlation Nu = 0.023 Re0.8 Pr0.4 is applicable, where the Nusselt Number (Nu) is defined on the basis of the pipe diameter. The pipe surface temperature at the exit is ________ oC (round off to the nearest integer).Correct answer is '321.267'. Can you explain this answer?
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Consider a hydrodynamically and thermally fully-developed, steady fluid flow of 1 kg/s in a uniformly heated pipe with diameter of 0.1 m and length of 40 m. A constant heat flux of magnitude 15000 W/m2 is imposed on the outer surface of the pipe. The bulk-mean temperature of the fluid at the entrance to the pipe is 200oC . The Reynolds number (Re) of the flow is 85000, and the Prandtl number (Pr) of the fluid is 5. The thermal conductivity and the specific heat of the fluid are 0.08 Wm-1K-1and 2600 Jkg-1K-1, respectively. The correlation Nu = 0.023 Re0.8 Pr0.4 is applicable, where the Nusselt Number (Nu) is defined on the basis of the pipe diameter. The pipe surface temperature at the exit is ________ oC (round off to the nearest integer).Correct answer is '321.267'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Consider a hydrodynamically and thermally fully-developed, steady fluid flow of 1 kg/s in a uniformly heated pipe with diameter of 0.1 m and length of 40 m. A constant heat flux of magnitude 15000 W/m2 is imposed on the outer surface of the pipe. The bulk-mean temperature of the fluid at the entrance to the pipe is 200oC . The Reynolds number (Re) of the flow is 85000, and the Prandtl number (Pr) of the fluid is 5. The thermal conductivity and the specific heat of the fluid are 0.08 Wm-1K-1and 2600 Jkg-1K-1, respectively. The correlation Nu = 0.023 Re0.8 Pr0.4 is applicable, where the Nusselt Number (Nu) is defined on the basis of the pipe diameter. The pipe surface temperature at the exit is ________ oC (round off to the nearest integer).Correct answer is '321.267'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a hydrodynamically and thermally fully-developed, steady fluid flow of 1 kg/s in a uniformly heated pipe with diameter of 0.1 m and length of 40 m. A constant heat flux of magnitude 15000 W/m2 is imposed on the outer surface of the pipe. The bulk-mean temperature of the fluid at the entrance to the pipe is 200oC . The Reynolds number (Re) of the flow is 85000, and the Prandtl number (Pr) of the fluid is 5. The thermal conductivity and the specific heat of the fluid are 0.08 Wm-1K-1and 2600 Jkg-1K-1, respectively. The correlation Nu = 0.023 Re0.8 Pr0.4 is applicable, where the Nusselt Number (Nu) is defined on the basis of the pipe diameter. The pipe surface temperature at the exit is ________ oC (round off to the nearest integer).Correct answer is '321.267'. Can you explain this answer?.
Consider a hydrodynamically and thermally fully-developed, steady fluid flow of 1 kg/s in a uniformly heated pipe with diameter of 0.1 m and length of 40 m. A constant heat flux of magnitude 15000 W/m2 is imposed on the outer surface of the pipe. The bulk-mean temperature of the fluid at the entrance to the pipe is 200oC . The Reynolds number (Re) of the flow is 85000, and the Prandtl number (Pr) of the fluid is 5. The thermal conductivity and the specific heat of the fluid are 0.08 Wm-1K-1and 2600 Jkg-1K-1, respectively. The correlation Nu = 0.023 Re0.8 Pr0.4 is applicable, where the Nusselt Number (Nu) is defined on the basis of the pipe diameter. The pipe surface temperature at the exit is ________ oC (round off to the nearest integer).Correct answer is '321.267'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Consider a hydrodynamically and thermally fully-developed, steady fluid flow of 1 kg/s in a uniformly heated pipe with diameter of 0.1 m and length of 40 m. A constant heat flux of magnitude 15000 W/m2 is imposed on the outer surface of the pipe. The bulk-mean temperature of the fluid at the entrance to the pipe is 200oC . The Reynolds number (Re) of the flow is 85000, and the Prandtl number (Pr) of the fluid is 5. The thermal conductivity and the specific heat of the fluid are 0.08 Wm-1K-1and 2600 Jkg-1K-1, respectively. The correlation Nu = 0.023 Re0.8 Pr0.4 is applicable, where the Nusselt Number (Nu) is defined on the basis of the pipe diameter. The pipe surface temperature at the exit is ________ oC (round off to the nearest integer).Correct answer is '321.267'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a hydrodynamically and thermally fully-developed, steady fluid flow of 1 kg/s in a uniformly heated pipe with diameter of 0.1 m and length of 40 m. A constant heat flux of magnitude 15000 W/m2 is imposed on the outer surface of the pipe. The bulk-mean temperature of the fluid at the entrance to the pipe is 200oC . The Reynolds number (Re) of the flow is 85000, and the Prandtl number (Pr) of the fluid is 5. The thermal conductivity and the specific heat of the fluid are 0.08 Wm-1K-1and 2600 Jkg-1K-1, respectively. The correlation Nu = 0.023 Re0.8 Pr0.4 is applicable, where the Nusselt Number (Nu) is defined on the basis of the pipe diameter. The pipe surface temperature at the exit is ________ oC (round off to the nearest integer).Correct answer is '321.267'. Can you explain this answer?.
Solutions for Consider a hydrodynamically and thermally fully-developed, steady fluid flow of 1 kg/s in a uniformly heated pipe with diameter of 0.1 m and length of 40 m. A constant heat flux of magnitude 15000 W/m2 is imposed on the outer surface of the pipe. The bulk-mean temperature of the fluid at the entrance to the pipe is 200oC . The Reynolds number (Re) of the flow is 85000, and the Prandtl number (Pr) of the fluid is 5. The thermal conductivity and the specific heat of the fluid are 0.08 Wm-1K-1and 2600 Jkg-1K-1, respectively. The correlation Nu = 0.023 Re0.8 Pr0.4 is applicable, where the Nusselt Number (Nu) is defined on the basis of the pipe diameter. The pipe surface temperature at the exit is ________ oC (round off to the nearest integer).Correct answer is '321.267'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mechanical Engineering.
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Consider a hydrodynamically and thermally fully-developed, steady fluid flow of 1 kg/s in a uniformly heated pipe with diameter of 0.1 m and length of 40 m. A constant heat flux of magnitude 15000 W/m2 is imposed on the outer surface of the pipe. The bulk-mean temperature of the fluid at the entrance to the pipe is 200oC . The Reynolds number (Re) of the flow is 85000, and the Prandtl number (Pr) of the fluid is 5. The thermal conductivity and the specific heat of the fluid are 0.08 Wm-1K-1and 2600 Jkg-1K-1, respectively. The correlation Nu = 0.023 Re0.8 Pr0.4 is applicable, where the Nusselt Number (Nu) is defined on the basis of the pipe diameter. The pipe surface temperature at the exit is ________ oC (round off to the nearest integer).Correct answer is '321.267'. Can you explain this answer?, a detailed solution for Consider a hydrodynamically and thermally fully-developed, steady fluid flow of 1 kg/s in a uniformly heated pipe with diameter of 0.1 m and length of 40 m. A constant heat flux of magnitude 15000 W/m2 is imposed on the outer surface of the pipe. The bulk-mean temperature of the fluid at the entrance to the pipe is 200oC . The Reynolds number (Re) of the flow is 85000, and the Prandtl number (Pr) of the fluid is 5. The thermal conductivity and the specific heat of the fluid are 0.08 Wm-1K-1and 2600 Jkg-1K-1, respectively. The correlation Nu = 0.023 Re0.8 Pr0.4 is applicable, where the Nusselt Number (Nu) is defined on the basis of the pipe diameter. The pipe surface temperature at the exit is ________ oC (round off to the nearest integer).Correct answer is '321.267'. Can you explain this answer? has been provided alongside types of Consider a hydrodynamically and thermally fully-developed, steady fluid flow of 1 kg/s in a uniformly heated pipe with diameter of 0.1 m and length of 40 m. A constant heat flux of magnitude 15000 W/m2 is imposed on the outer surface of the pipe. The bulk-mean temperature of the fluid at the entrance to the pipe is 200oC . The Reynolds number (Re) of the flow is 85000, and the Prandtl number (Pr) of the fluid is 5. The thermal conductivity and the specific heat of the fluid are 0.08 Wm-1K-1and 2600 Jkg-1K-1, respectively. The correlation Nu = 0.023 Re0.8 Pr0.4 is applicable, where the Nusselt Number (Nu) is defined on the basis of the pipe diameter. The pipe surface temperature at the exit is ________ oC (round off to the nearest integer).Correct answer is '321.267'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Consider a hydrodynamically and thermally fully-developed, steady fluid flow of 1 kg/s in a uniformly heated pipe with diameter of 0.1 m and length of 40 m. A constant heat flux of magnitude 15000 W/m2 is imposed on the outer surface of the pipe. The bulk-mean temperature of the fluid at the entrance to the pipe is 200oC . The Reynolds number (Re) of the flow is 85000, and the Prandtl number (Pr) of the fluid is 5. The thermal conductivity and the specific heat of the fluid are 0.08 Wm-1K-1and 2600 Jkg-1K-1, respectively. The correlation Nu = 0.023 Re0.8 Pr0.4 is applicable, where the Nusselt Number (Nu) is defined on the basis of the pipe diameter. The pipe surface temperature at the exit is ________ oC (round off to the nearest integer).Correct answer is '321.267'. Can you explain this answer? tests, examples and also practice Mechanical Engineering tests.
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