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A cylindrical shell 90 cm long and 20 cm internal diameter having thickness of metal as 8 mm is filled with fluid at atmospheric pressure. If an additional 20 cm3 of fluid is pumped into the cylinder, find the pressure (in MPa) exerted by the fluid on the cylinder. Take E = 2 × 105 N/mm2 and μ = 0.3.
Correct answer is between '5.8,6.05'. Can you explain this answer?
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A cylindrical shell 90 cm long and 20 cm internal diameter having thic...
We can use the formula for hoop stress in a cylindrical shell:
σ = pd/2t
where σ is the stress, p is the pressure, d is the diameter, and t is the thickness.
First, we need to find the external diameter of the cylinder, which is:
D = d + 2t
D = 20 cm + 2(8 mm)
D = 20.16 cm
Next, we can find the initial volume of the fluid in the cylinder:
V = πr^2h
V = π(10 cm)^2(90 cm)
V = 28,274 cm^3
Since the cylinder is filled at atmospheric pressure, we can assume the pressure is 1 atm or 101.3 kPa.
Now, we can find the stress on the cylinder due to the initial volume of fluid:
σ1 = pd/2t
σ1 = (101.3 kPa)(20.16 cm)/(2)(8 mm)
σ1 = 253.25 kPa
When the additional 20 cm^3 of fluid is pumped into the cylinder, the new volume of fluid is:
V2 = V1 + 20 cm^3
V2 = 28,274 cm^3 + 20 cm^3
V2 = 28,294 cm^3
We can use the formula for volume of a cylinder to find the new height of the fluid:
V = πr^2h
28,294 cm^3 = π(10 cm)^2h
h = 28.29 cm
Now, we can find the new pressure on the cylinder:
σ2 = pd/2t
σ2 = p(20.16 cm)/(2)(8 mm)
σ2 = 5p
We know that the change in volume of the fluid is:
ΔV = 20 cm^3
We can use the bulk modulus of the fluid to find the change in pressure due to this change in volume:
ΔP = -VΔB/βV
ΔP = -(20 cm^3)(2 MPa)/(2.1x10^9 Pa)
ΔP = -0.019 kPa
The negative sign indicates that the pressure decreased due to the increase in volume.
Finally, we can find the new pressure exerted by the fluid on the cylinder:
σ2 + ΔP = 5p - 0.019 kPa
We can now solve for p:
p = (σ2 + ΔP)/5
p = (5p - 0.019 kPa)/5
4p = 0.019 kPa
p = 0.0048 MPa
Therefore, the pressure exerted by the fluid on the cylinder is 0.0048 MPa.
σ = pd/2t
where σ is the stress, p is the pressure, d is the diameter, and t is the thickness.
First, we need to find the external diameter of the cylinder, which is:
D = d + 2t
D = 20 cm + 2(8 mm)
D = 20.16 cm
Next, we can find the initial volume of the fluid in the cylinder:
V = πr^2h
V = π(10 cm)^2(90 cm)
V = 28,274 cm^3
Since the cylinder is filled at atmospheric pressure, we can assume the pressure is 1 atm or 101.3 kPa.
Now, we can find the stress on the cylinder due to the initial volume of fluid:
σ1 = pd/2t
σ1 = (101.3 kPa)(20.16 cm)/(2)(8 mm)
σ1 = 253.25 kPa
When the additional 20 cm^3 of fluid is pumped into the cylinder, the new volume of fluid is:
V2 = V1 + 20 cm^3
V2 = 28,274 cm^3 + 20 cm^3
V2 = 28,294 cm^3
We can use the formula for volume of a cylinder to find the new height of the fluid:
V = πr^2h
28,294 cm^3 = π(10 cm)^2h
h = 28.29 cm
Now, we can find the new pressure on the cylinder:
σ2 = pd/2t
σ2 = p(20.16 cm)/(2)(8 mm)
σ2 = 5p
We know that the change in volume of the fluid is:
ΔV = 20 cm^3
We can use the bulk modulus of the fluid to find the change in pressure due to this change in volume:
ΔP = -VΔB/βV
ΔP = -(20 cm^3)(2 MPa)/(2.1x10^9 Pa)
ΔP = -0.019 kPa
The negative sign indicates that the pressure decreased due to the increase in volume.
Finally, we can find the new pressure exerted by the fluid on the cylinder:
σ2 + ΔP = 5p - 0.019 kPa
We can now solve for p:
p = (σ2 + ΔP)/5
p = (5p - 0.019 kPa)/5
4p = 0.019 kPa
p = 0.0048 MPa
Therefore, the pressure exerted by the fluid on the cylinder is 0.0048 MPa.
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A cylindrical shell 90 cm long and 20 cm internal diameter having thickness of metal as 8 mm is filled with fluid at atmospheric pressure. If an additional 20 cm3of fluid is pumped into the cylinder, find the pressure (in MPa) exerted by the fluid on the cylinder. Take E = 2 × 105N/mm2and μ = 0.3.Correct answer is between '5.8,6.05'. Can you explain this answer?
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A cylindrical shell 90 cm long and 20 cm internal diameter having thickness of metal as 8 mm is filled with fluid at atmospheric pressure. If an additional 20 cm3of fluid is pumped into the cylinder, find the pressure (in MPa) exerted by the fluid on the cylinder. Take E = 2 × 105N/mm2and μ = 0.3.Correct answer is between '5.8,6.05'. 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 A cylindrical shell 90 cm long and 20 cm internal diameter having thickness of metal as 8 mm is filled with fluid at atmospheric pressure. If an additional 20 cm3of fluid is pumped into the cylinder, find the pressure (in MPa) exerted by the fluid on the cylinder. Take E = 2 × 105N/mm2and μ = 0.3.Correct answer is between '5.8,6.05'. 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 A cylindrical shell 90 cm long and 20 cm internal diameter having thickness of metal as 8 mm is filled with fluid at atmospheric pressure. If an additional 20 cm3of fluid is pumped into the cylinder, find the pressure (in MPa) exerted by the fluid on the cylinder. Take E = 2 × 105N/mm2and μ = 0.3.Correct answer is between '5.8,6.05'. Can you explain this answer?.
A cylindrical shell 90 cm long and 20 cm internal diameter having thickness of metal as 8 mm is filled with fluid at atmospheric pressure. If an additional 20 cm3of fluid is pumped into the cylinder, find the pressure (in MPa) exerted by the fluid on the cylinder. Take E = 2 × 105N/mm2and μ = 0.3.Correct answer is between '5.8,6.05'. 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 A cylindrical shell 90 cm long and 20 cm internal diameter having thickness of metal as 8 mm is filled with fluid at atmospheric pressure. If an additional 20 cm3of fluid is pumped into the cylinder, find the pressure (in MPa) exerted by the fluid on the cylinder. Take E = 2 × 105N/mm2and μ = 0.3.Correct answer is between '5.8,6.05'. 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 A cylindrical shell 90 cm long and 20 cm internal diameter having thickness of metal as 8 mm is filled with fluid at atmospheric pressure. If an additional 20 cm3of fluid is pumped into the cylinder, find the pressure (in MPa) exerted by the fluid on the cylinder. Take E = 2 × 105N/mm2and μ = 0.3.Correct answer is between '5.8,6.05'. Can you explain this answer?.
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