Fluid Mechanics: Properties and Calculations

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Questions and Answers

A cylindrical tank is filled with a liquid. The tank's diameter and height are 80 cm and 90 cm, respectively. The tank with the liquid weighs 420 kg, while the empty tank weighs 40 kg. What is the mass density of the liquid?

  • 840 kg/m³ (correct)
  • 631 kg/m³
  • 529 kg/m³
  • 921 kg/m³

In a scenario where you need to determine the pressure difference between two points (A and B) in a complex fluid system involving benzene, mercury, kerosene, and glycerin, which of the following correctly accounts for the specific gravities and heights of each fluid layer?

  • The pressure difference can be found by only considering the specific gravity of each fluid.
  • The pressure difference is solely dependent on the height of the mercury column.
  • You should subtract the products of specific gravity, density of water, and height for each fluid layer between A and B, summing them up. (correct)
  • You should add the products of specific gravity, density of water, and height for each fluid layer regardless of position between A and B.

A glass capillary tube with a diameter of 2 mm is placed on top of a mercury layer. Given that the surface tension of mercury is 0.514 N/m and its contact angle with the glass is 130°, what is the height of the capillary depression?

  • 8.09 mm
  • 7.65 mm
  • 4.95 mm (correct)
  • 5.20 mm

Nitrogen gas at 30°C is under a pressure of 560 kPa. Assuming the gas constant for nitrogen is 296.8 J/kg·K, calculate its specific volume.

<p>0.136 m³/kg (D)</p> Signup and view all the answers

A triangular gate with a horizontal base of 1.5 m and an altitude of 2 m is inclined at 45° from the vertical, with the vertex pointing upward. The hinged base of the gate is 3 m below the water surface. What is the total hydrostatic force on the gate?

<p>37.21 kN (A)</p> Signup and view all the answers

A vertical rectangular gate 1.5 m wide and 3 m high is submerged in water with its bottom edge submerged 2 m below the water surface. Find the hydrostatic force acting on one side of the gate.

<p>42.27 kN (A)</p> Signup and view all the answers

A 5000 kg iceberg floats in seawater. The density of the iceberg is 890 kg/m³, and the density of seawater is 1030 kg/m³. What is the volume of the ice above the surface?

<p>0.663 m³ (B)</p> Signup and view all the answers

A block of wood floats in water with 5 cm projecting above the water surface. When placed in glycerine of specific gravity 1.35, the block projects 7.5 cm above the liquid. Determine the total length of the wood.

<p>17.22 cm (B)</p> Signup and view all the answers

A stone weighs 280 N in alcohol (specific gravity = 0.8) and 220 N in glycerine (specific gravity = 1.25). What is the volume of the stone?

<p>0.01359 m³ (C)</p> Signup and view all the answers

A masonry dam of trapezoidal cross-section, with one end face vertical, has a thickness of 0.6 m at the top and 3 m at the bottom. It is 6.75 m high, and the vertical face is subjected to water pressure, with the water standing 4.6 m above the base at the upstream side. The hydrostatic uplift varies uniformly from 50% at the heel to zero at the toe. Assume that the specific gravity of the concrete is 2.4. Find the vertical component of the foundation reaction.

<p>522.52 kN (D)</p> Signup and view all the answers

Flashcards

Mass Density

Mass per unit volume. ρ = m/V

Specific Volume

Volume per unit mass. ν = 1/ρ

Specific Gravity

Ratio of fluid density to water density. SG = ρ_fluid / ρ_water

Specific Weight

Weight per unit volume, calculated as weight divided by volume.

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Pressure Variation Formula

∆P = γ * h

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Pressure Difference

Pressure difference between two points in a fluid column.

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Capillary Action

Capillary rise or depression in a tube. h = (4 * T * cosθ) / (ρ * g * d)

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Ideal Gas Law

PV = mRT

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Hydrostatic Force

The total hydrostatic force on a submerged gate.

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Location of Hydrostatic Force

Vertical distance from the liquid surface to the center of pressure.

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Study Notes

Fluid Mechanics - Fluid Properties

  • A cylindrical tank with a diameter of 80 cm and a height of 90 cm is filled with a certain liquid.
  • The tank and liquid weigh 420 kg, while the empty tank weighs 40 kg.

Mass Density

  • Calculated as 420 kg - 40 kg divided by the volume
  • Mass density = 529 kg/m3

Specific Volume

  • Calculated to be 0.00119 m³/kg

Specific Gravity

  • Calculated to be 0.84

Specific Weight

  • Calculated as 8.24 kN/m³

Gravity Force

  • The gravity force of the liquid is 3727.8 N

Pressure at the Bottom of the Tank

  • Pressure at the bottom of the tank is 7.416 kPa

Oil Height Equivalent to Mercury Height

  • 760 mm Hg is equivalent to 12920 mm of oil

Pressure Difference Between Points A and B

  • The pressure difference (PA - PB) is 10.53 kPa.

Capillary Depression

  • For a glass capillary tube with a 2 mm diameter placed on mercury, the height of capillary depression is 4.95 mm

Specific Volume of Nitrogen Gas

  • The specific volume of nitrogen gas at 30°C under 560 kPa pressure is 0.136 m³

Fluid Mechanics - Hydrostatic Pressure

Total Hydrostatic Force on the Gate

  • Total hydrostatic force on the gate is 37.21 kN

Vertical Force to Submerge Iceberg

  • The vertical force required to fully submerge the iceberg is 1.395 m

Normal Force at Vertex

  • Normal force to be applied to the vertex of the gate to keep it closed is 9.67 kN

Horizontal Component of Hydrostatic Force

  • The horizontal component of the hydrostatic force acting on the quarter-circular gate BC is 956.48 kN

Total Hydrostatic Force

  • The total hydrostatic force acting on the quarter-circular gate BC is 1508.46 kN

Location of Vertical Component

  • The location of the vertical component of the hydrostatic force from point O is 2.152 m

Hydrostatic Force on Rectangular Gate

  • The hydrostatic force acting on one side of a rectangular gate is 42.27 kN.

Location of Force

  • The location of the resultant force is located 0.67 m from the bottom of a rectangular gate

Hydrostatic Force on Semi-Circular Gate

  • The hydrostatic force acting on the semi-circular gate AB is 811.3 kN

Location of Force

  • The location of the point of application for the force from the oil surface is 4.9 m

Reaction at Roller A

  • The reaction of the roller at A is 396.35 kN

Fluid Mechanics - Buoyancy

Volume of Iceberg Above Surface

  • The volume of the iceberg above the surface is 0.663 m³

Vertical Force to Submerge Iceberg

  • The vertical force to fully submerge the iceberg is 10.738 kN

Length of Wood Block

  • The total length of the wood block is 17.22 cm

Specific Gravity of Wood

  • The specific gravity of the wood is 0.45

Projection in Seawater

  • The projection of the wood in seawater would be 6.32 cm

Volume of Stone

  • The volume of the stone is 0.01227 m³

Specific Weight of Stone

  • The specific weight of the stone is 35.67 kN/m³

Relative Density of Stone

  • The relative density of the stone is 2.5

Buoyant Force on Wood Block

  • The buoyant force on the wood block is 0.110 N

Tension in Rope

  • The tension in the rope is 0.110 N

Specific Weight of Metal Part

  • The specific weight of the metal part is 17.91 kN/m³

Fluid Mechanics - Stability

Metacentric Height in Tilted Position

  • The metacentric height in the tilted position is 6 m

Type of Moment Generated

  • A righting moment is generated

Magnitude of Moment

  • The magnitude of the moment is 40,000 kNm

Submerged Depth

  • The submerged depth of the wooden cone is 19 cm

Distance from Metacenter to Center of Buoyancy

  • The distance from the metacenter to the center of buoyancy is 1.791 cm

Initial Metacentric Height

  • The initial metacentric height of the scow is 1.41 m

Final Metacentric Height

  • The final metacentric height when one end is submerged is 1.41 m

Initial Metacentric Height Against Rolling Axis

  • (The answer is not present)

Fluid Mechanics - Dams

Vertical Component of Foundation Reaction

  • The vertical component of the foundation reaction is 252.22 kN

Intersection of Vertical Reaction

  • The vertical reaction will intersect the base at 1.57 m

Factor of Safety Against Overturning

  • The factor of safety against overturning is 3.5

Factor of Safety Against Sliding

  • The factor of safety against sliding, assuming μ = 0.6, is 3.5

Maximum Pressure Along the Base

  • The maximum pressure along the base is 112.56 kPa

Minimum Pressure Along the Base

  • The minimum pressure along the base is 55.49 kPa

New Base Length

  • The new base for the dam to maintain the same factor of safety against overturning if filled is 5.1 m

Height of Water

  • The height of water on the vertical side causing the vertical reaction to one third of the distance, is 6.50 m

Shearing Stress at Base

  • The shearing stress at the base is 45.3 kPa

Pressure at Toe

  • The pressure at the toe is 171.20 kPa

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