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1. A wooden cylinder of sp. gr. = 0.6 and circular in cross-section is required to float in oil (sp. gr. = 0.90). Find the L/D ratio for the cylinder to float with its longitudinal axis vertical in oil, where L is the height of cylinder and D is its diameter.?
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1. A wooden cylinder of sp. gr. = 0.6 and circular in cross-section is...
Given data:
- Specific gravity of wooden cylinder (ρw) = 0.6
- Specific gravity of oil (ρo) = 0.9
We need to find the L/D ratio for the cylinder to float in oil with its longitudinal axis vertical.
Assumptions:
- The cylinder is a perfect circular cylinder.
- The entire cylinder is completely submerged in oil.
- There is no friction between the cylinder and oil.
Solution:
1. Buoyancy force acting on the cylinder:
- The buoyancy force (FB) acting on the cylinder is given by the Archimedes principle:
FB = ρo * g * V
where,
ρo = specific gravity of oil
g = acceleration due to gravity
V = volume of the cylinder
- The volume of the cylinder is given by:
V = π * D^2 * L / 4
where,
D = diameter of the cylinder
L = height of the cylinder
2. Weight of the cylinder:
- The weight of the cylinder (W) is given by:
W = ρw * g * V
where,
ρw = specific gravity of the wooden cylinder
3. Condition for floating:
- For the cylinder to float in oil, the buoyancy force should be equal to or greater than the weight of the cylinder.
FB ≥ W
- Substituting the values of FB and W, we get:
ρo * g * V ≥ ρw * g * V
- Simplifying, we get:
L/D ≥ ρw / ρo
4. L/D ratio:
- The minimum value of L/D required for the cylinder to float in oil is given by:
L/D = ρw / ρo
- Substituting the given values, we get:
L/D = 0.6 / 0.9 = 0.67
Therefore, the L/D ratio for the wooden cylinder to float in oil with its longitudinal axis vertical is 0.67.
- Specific gravity of wooden cylinder (ρw) = 0.6
- Specific gravity of oil (ρo) = 0.9
We need to find the L/D ratio for the cylinder to float in oil with its longitudinal axis vertical.
Assumptions:
- The cylinder is a perfect circular cylinder.
- The entire cylinder is completely submerged in oil.
- There is no friction between the cylinder and oil.
Solution:
1. Buoyancy force acting on the cylinder:
- The buoyancy force (FB) acting on the cylinder is given by the Archimedes principle:
FB = ρo * g * V
where,
ρo = specific gravity of oil
g = acceleration due to gravity
V = volume of the cylinder
- The volume of the cylinder is given by:
V = π * D^2 * L / 4
where,
D = diameter of the cylinder
L = height of the cylinder
2. Weight of the cylinder:
- The weight of the cylinder (W) is given by:
W = ρw * g * V
where,
ρw = specific gravity of the wooden cylinder
3. Condition for floating:
- For the cylinder to float in oil, the buoyancy force should be equal to or greater than the weight of the cylinder.
FB ≥ W
- Substituting the values of FB and W, we get:
ρo * g * V ≥ ρw * g * V
- Simplifying, we get:
L/D ≥ ρw / ρo
4. L/D ratio:
- The minimum value of L/D required for the cylinder to float in oil is given by:
L/D = ρw / ρo
- Substituting the given values, we get:
L/D = 0.6 / 0.9 = 0.67
Therefore, the L/D ratio for the wooden cylinder to float in oil with its longitudinal axis vertical is 0.67.
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1. A wooden cylinder of sp. gr. = 0.6 and circular in cross-section is required to float in oil (sp. gr. = 0.90). Find the L/D ratio for the cylinder to float with its longitudinal axis vertical in oil, where L is the height of cylinder and D is its diameter.?
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1. A wooden cylinder of sp. gr. = 0.6 and circular in cross-section is required to float in oil (sp. gr. = 0.90). Find the L/D ratio for the cylinder to float with its longitudinal axis vertical in oil, where L is the height of cylinder and D is its diameter.? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about 1. A wooden cylinder of sp. gr. = 0.6 and circular in cross-section is required to float in oil (sp. gr. = 0.90). Find the L/D ratio for the cylinder to float with its longitudinal axis vertical in oil, where L is the height of cylinder and D is its diameter.? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 1. A wooden cylinder of sp. gr. = 0.6 and circular in cross-section is required to float in oil (sp. gr. = 0.90). Find the L/D ratio for the cylinder to float with its longitudinal axis vertical in oil, where L is the height of cylinder and D is its diameter.?.
1. A wooden cylinder of sp. gr. = 0.6 and circular in cross-section is required to float in oil (sp. gr. = 0.90). Find the L/D ratio for the cylinder to float with its longitudinal axis vertical in oil, where L is the height of cylinder and D is its diameter.? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about 1. A wooden cylinder of sp. gr. = 0.6 and circular in cross-section is required to float in oil (sp. gr. = 0.90). Find the L/D ratio for the cylinder to float with its longitudinal axis vertical in oil, where L is the height of cylinder and D is its diameter.? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 1. A wooden cylinder of sp. gr. = 0.6 and circular in cross-section is required to float in oil (sp. gr. = 0.90). Find the L/D ratio for the cylinder to float with its longitudinal axis vertical in oil, where L is the height of cylinder and D is its diameter.?.
Solutions for 1. A wooden cylinder of sp. gr. = 0.6 and circular in cross-section is required to float in oil (sp. gr. = 0.90). Find the L/D ratio for the cylinder to float with its longitudinal axis vertical in oil, where L is the height of cylinder and D is its diameter.? in English & in Hindi are available as part of our courses for GATE.
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1. A wooden cylinder of sp. gr. = 0.6 and circular in cross-section is required to float in oil (sp. gr. = 0.90). Find the L/D ratio for the cylinder to float with its longitudinal axis vertical in oil, where L is the height of cylinder and D is its diameter.?, a detailed solution for 1. A wooden cylinder of sp. gr. = 0.6 and circular in cross-section is required to float in oil (sp. gr. = 0.90). Find the L/D ratio for the cylinder to float with its longitudinal axis vertical in oil, where L is the height of cylinder and D is its diameter.? has been provided alongside types of 1. A wooden cylinder of sp. gr. = 0.6 and circular in cross-section is required to float in oil (sp. gr. = 0.90). Find the L/D ratio for the cylinder to float with its longitudinal axis vertical in oil, where L is the height of cylinder and D is its diameter.? theory, EduRev gives you an
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