### Common Fluid Properties

• Define the terms in relation to fluid mechanics such as density, specific gravity, viscosity and vapor pressure.

Mass Density ($\rho$) is defined as the mass of substance per unit volume.

$\rho = \frac{m}{V}$

Specific gravity (s) of a fluid is the dimensionless number. $s = \frac{\rho_{\mathrm{\ fluid}}}{\rho_{\mathrm{\ standard\ fluid}}}$ Specific Weight ($\gamma$) is defined as the weight per unit volume.

$\gamma = \rho g \ \mathrm{or}\ \rho = \frac{\gamma}{g}$ Specific volume (v) is the volume occupied by a unit mass of fluid. $\mathrm{v} = \frac{1}{\rho}$ Viscosity ($\mu$) of a fluid measures its resistance to flow under an applied shear stress. Representative units for viscosity are Pa.s (also known as poise designated by P). The centipoise (cP), one hundredth of a poise, is also a convenient unit, since the viscosity of water at room temperature is approximately 1 centipoise.
Kinematic viscosity ($\nu$) is the ratio of the viscosity to the density. $\nu = \frac{\mu}{\rho}$

Vapor Pressure: The pressure at which a liquid will boil is called its vapor pressure.

### Solved Example:

#### 60-1-01

Fluid is a substance that: (TANGEDCO AE EC 2018)

Solution:
Fluids include liquids and gases. While gases always expand till they fill any container, liquids do not.
One of the defining characteristics of fluids is they cannot resist shear stresses (like what solids can), and on application of shear stresses, they start deforming or flowing.

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Practical fluids:

Solution:
Practically, fluids have properties such as viscosity, compressibility as well as surface tension.

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Density of water is maximum at:

Solution:

Water exists in liquid format between 0-100 C. Generally density of liquid increases as temperature is reduced. However, water has a small exception. Water displays abnormal behavior between 0-4 Degree Celsius when the density actually decreases as the temperate decreases.

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#### 60-1-04

Poise is the unit of: (SSC JE ME Paper 4- Jan 2018 Morning)

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#### 60-1-05

Choose the correct relationship:

Solution:
$\mathrm{Kinematic\ viscosity} = \dfrac{\mathrm{Dynamic\ Viscosity}}{\mathrm{density}}$ $\mathrm{Dynamic\ viscosity} = \mathrm{Kinematic\ Viscosity} \times \mathrm{density}$

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Choose the wrong statement:

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Kinematic viscosity is equal to: (UPSSSC JE Mech 2015- Paper 2)

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Viscosity of water in comparison to mercury is: (ISRO Scientist Mechanical 2013)

Solution:

Dynamic viscosity of water at 27$^\circ C$ = 0.89 centipoise whereas that of mercury at same temperature = 1.53 centipoise, so dynamic viscosity of mercury is higher than water.

However, kinematic viscosity is ratio of dynamic viscosity to density and mercury is 13.6 denser than water.

Once you divide by higher density of mercury, the kinematic viscosity of mercury is much lesser than water. (water = $1 \times 10^{-6} m^2/s$ compared to mercury = $0.115 \times 10^{-6} m^2/s$)

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#### 60-1-09

Surface tension has the units of: (MPSC AMVI Official Paper 1: Set A/2017)

Solution:

Surface tension is force per unit length, hence its units will be N/m.

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#### 60-1-10

Property of a fluid by which molecules of different kinds of fluids are attracted to each other is called:

Solution:

Adhesion is attraction between unlike molecules whereas cohesion is attraction between like molecules.

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Specific weight of water in S.I. units is equal to:

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Which of the following is dimensionless? (NPCIL SA/ST ME GJ Nov 2019- Shift I)

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The tendency of a liquid surface to contract is due to the following property:

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A fluid in equilibrium can't sustain: (ISRO Scientist Civil 2015)

Surface tension:

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The property of fluid by virtue of which it offers resistance to shear is called: (ISRO VSSC Technical Asst. Mechanical April 2012)

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#### 60-1-17

Kinematic viscosity is dependent upon:

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#### 60-1-18

Surface energy per unit area of a surface is numerically equal to:

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Choose the wrong statement:

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#### 60-1-20

Surface energy per unit area of a surface is numerically equal to:

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If 850 kg liquid occupies volume of one cubic meter, means 0.85 represents its:

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The property by virtue of which a liquid opposes relative motion between its different layers is called:

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The process of diffusion of one liquid into the other through a semi-permeable membrane is called:

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Free surface of a liquid tends to contract to the smallest possible area due to force of:

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The kinematic viscosity is the: (AFCAT EKT Mechanical Paper 4- Set 01/2014)

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A piece of metal of specific gravity 7 floats in mercury of specific gravity 13.6. What fraction of its volume is under mercury ? (SSC Jr. Engg. Mechanical 2018)

If 5.6$m^3$ of oil weighs 46800 N, What is the relative density of the oil?
$\mathrm{Mass} = \dfrac{W}{g} = \dfrac{46800}{9.8} =4770.61\ kg$ $\mathrm{Density} = \dfrac{m}{V} = \dfrac{4770.61}{5.6} =851.90\ kg/m^3$ $\mathrm{Relative\ density} = \dfrac{\rho_{\ \mathrm{fluid}}}{\rho_{\ \mathrm{water}}} = \dfrac{851.9}{1000} = 0.852$