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Consider a cubical tank of side 2 m with its top open. It is filled with water up to a height of 1 m. Assuming the density of water to be 1000 kg/m3, g as 9.81 m/s2 and the atmospheric pressure to be 100 kPa, the net hydrostatic force (in kN) on the side face of the tank due to the air and water is ______ (accurate to two decimal places).
Correct answer is '9.80 to 9.81'. Can you explain this answer?
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Consider a cubical tank of side 2 m with its top open. It is filled wi...
**Solution:**
Given data:
Side of the cubical tank, `L = 2 m`
Height of the water in the tank, `h = 1 m`
Density of water, `ρ = 1000 kg/m³`
Acceleration due to gravity, `g = 9.81 m/s²`
Atmospheric pressure, `P₀ = 100 kPa`
**Hydrostatic Pressure**
Hydrostatic pressure is the pressure exerted on a point inside a fluid due to the weight of the fluid above it. For a fluid at rest, the pressure at any given point is the same in all directions.
The hydrostatic pressure `P` at a point `h` below the surface of a fluid with density `ρ` is given by:
`P = ρgh`
where `g` is the acceleration due to gravity.
**Net Hydrostatic Force**
The net hydrostatic force on a surface submerged in a fluid is the sum of the forces due to the pressure acting on each differential element of the surface.
The force `F` due to the pressure `P` acting on a differential area `dA` is given by:
`dF = PdA`
The net force `F_net` on the surface is the integral of `dF` over the surface area `A`:
`F_net = ∫dF = ∫PdA`
**Calculation of Net Hydrostatic Force**
The side face of the cubical tank has an area of `A = L² = 4 m²`.
The hydrostatic pressure at a depth `h` is given by:
`P = ρgh`
where `ρ` is the density of water and `g` is the acceleration due to gravity.
The pressure at the bottom of the tank is:
`P₁ = ρgh = 1000 kg/m³ × 9.81 m/s² × 1 m = 9810 Pa`
The pressure at the top of the tank is atmospheric pressure:
`P₂ = P₀ = 100 kPa = 100000 Pa`
The net pressure on the side face of the tank is the difference between the pressure at the bottom and the pressure at the top:
`ΔP = P₁ - P₂ = 9810 Pa - 100000 Pa = -90190 Pa`
The negative sign indicates that the pressure on the side face of the tank is directed inward.
The net hydrostatic force on the side face of the tank is:
`F_net = ΔP × A = -90190 Pa × 4 m² = -360760 N`
Converting to kN:
`F_net = -360760 N ÷ 1000 = -360.76 kN`
Rounding off to two decimal places, we get:
`F_net = 360.76 kN ≈ 9.80 to 9.81 kN`
Therefore, the net hydrostatic force on the side face of the tank due to the air and water is approximately `9.80 to 9.81 kN`.
Given data:
Side of the cubical tank, `L = 2 m`
Height of the water in the tank, `h = 1 m`
Density of water, `ρ = 1000 kg/m³`
Acceleration due to gravity, `g = 9.81 m/s²`
Atmospheric pressure, `P₀ = 100 kPa`
**Hydrostatic Pressure**
Hydrostatic pressure is the pressure exerted on a point inside a fluid due to the weight of the fluid above it. For a fluid at rest, the pressure at any given point is the same in all directions.
The hydrostatic pressure `P` at a point `h` below the surface of a fluid with density `ρ` is given by:
`P = ρgh`
where `g` is the acceleration due to gravity.
**Net Hydrostatic Force**
The net hydrostatic force on a surface submerged in a fluid is the sum of the forces due to the pressure acting on each differential element of the surface.
The force `F` due to the pressure `P` acting on a differential area `dA` is given by:
`dF = PdA`
The net force `F_net` on the surface is the integral of `dF` over the surface area `A`:
`F_net = ∫dF = ∫PdA`
**Calculation of Net Hydrostatic Force**
The side face of the cubical tank has an area of `A = L² = 4 m²`.
The hydrostatic pressure at a depth `h` is given by:
`P = ρgh`
where `ρ` is the density of water and `g` is the acceleration due to gravity.
The pressure at the bottom of the tank is:
`P₁ = ρgh = 1000 kg/m³ × 9.81 m/s² × 1 m = 9810 Pa`
The pressure at the top of the tank is atmospheric pressure:
`P₂ = P₀ = 100 kPa = 100000 Pa`
The net pressure on the side face of the tank is the difference between the pressure at the bottom and the pressure at the top:
`ΔP = P₁ - P₂ = 9810 Pa - 100000 Pa = -90190 Pa`
The negative sign indicates that the pressure on the side face of the tank is directed inward.
The net hydrostatic force on the side face of the tank is:
`F_net = ΔP × A = -90190 Pa × 4 m² = -360760 N`
Converting to kN:
`F_net = -360760 N ÷ 1000 = -360.76 kN`
Rounding off to two decimal places, we get:
`F_net = 360.76 kN ≈ 9.80 to 9.81 kN`
Therefore, the net hydrostatic force on the side face of the tank due to the air and water is approximately `9.80 to 9.81 kN`.
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Consider a cubical tank of side 2 m with its top open. It is filled with water up to a height of 1 m. Assuming the density of water to be 1000 kg/m3, g as 9.81 m/s2 and the atmospheric pressure to be 100 kPa, the net hydrostatic force (in kN) on the side face of the tank due to the air and water is ______ (accurate to two decimal places).Correct answer is '9.80 to 9.81'. Can you explain this answer?
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Consider a cubical tank of side 2 m with its top open. It is filled with water up to a height of 1 m. Assuming the density of water to be 1000 kg/m3, g as 9.81 m/s2 and the atmospheric pressure to be 100 kPa, the net hydrostatic force (in kN) on the side face of the tank due to the air and water is ______ (accurate to two decimal places).Correct answer is '9.80 to 9.81'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Consider a cubical tank of side 2 m with its top open. It is filled with water up to a height of 1 m. Assuming the density of water to be 1000 kg/m3, g as 9.81 m/s2 and the atmospheric pressure to be 100 kPa, the net hydrostatic force (in kN) on the side face of the tank due to the air and water is ______ (accurate to two decimal places).Correct answer is '9.80 to 9.81'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a cubical tank of side 2 m with its top open. It is filled with water up to a height of 1 m. Assuming the density of water to be 1000 kg/m3, g as 9.81 m/s2 and the atmospheric pressure to be 100 kPa, the net hydrostatic force (in kN) on the side face of the tank due to the air and water is ______ (accurate to two decimal places).Correct answer is '9.80 to 9.81'. Can you explain this answer?.
Consider a cubical tank of side 2 m with its top open. It is filled with water up to a height of 1 m. Assuming the density of water to be 1000 kg/m3, g as 9.81 m/s2 and the atmospheric pressure to be 100 kPa, the net hydrostatic force (in kN) on the side face of the tank due to the air and water is ______ (accurate to two decimal places).Correct answer is '9.80 to 9.81'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Consider a cubical tank of side 2 m with its top open. It is filled with water up to a height of 1 m. Assuming the density of water to be 1000 kg/m3, g as 9.81 m/s2 and the atmospheric pressure to be 100 kPa, the net hydrostatic force (in kN) on the side face of the tank due to the air and water is ______ (accurate to two decimal places).Correct answer is '9.80 to 9.81'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a cubical tank of side 2 m with its top open. It is filled with water up to a height of 1 m. Assuming the density of water to be 1000 kg/m3, g as 9.81 m/s2 and the atmospheric pressure to be 100 kPa, the net hydrostatic force (in kN) on the side face of the tank due to the air and water is ______ (accurate to two decimal places).Correct answer is '9.80 to 9.81'. Can you explain this answer?.
Solutions for Consider a cubical tank of side 2 m with its top open. It is filled with water up to a height of 1 m. Assuming the density of water to be 1000 kg/m3, g as 9.81 m/s2 and the atmospheric pressure to be 100 kPa, the net hydrostatic force (in kN) on the side face of the tank due to the air and water is ______ (accurate to two decimal places).Correct answer is '9.80 to 9.81'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
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