Fluid Mechanics - 1

Specific Weight:

\(\gamma = \rho g = 7.85 \Rightarrow \rho = \frac{{7.85 \times {{10}^3}}}{{10}} = 785\)

Specific gravity:

\(s = \frac{\rho }{{{\rho _{water}}}} = \frac{{785}}{{1000}} = 0.8\)

P=ρgQH=1000×9.81×0.025×30=7357.5WP=ρgQH=1000×9.81×0.025×30=7357.5W

Power required:

Velocity Potential function (ϕ) is given as = x² - y²

For continuity to be satisfied

-2 + 2 = 0

(Hence satisfied)

A fluid is rotating at constant angular velocity ω about the central vertical axis of a cylindrical container. The variation of pressure in the radial direction is given by

It is given that the pressure at the axis of rotation is P_c.

Therefore, the required pressure at any point r is

P = ρgh

h = z

P = ρgz

200 × 10³ = 1.59 × 1000 × 9.81 × z

z = 12.82 metres

Where P = Pressure (pascal)

ρ = density of fluid (kg/m³)

g = acceleration due to gravity (m/s²)

h = height of liquid column (metres)

As temperature increases, randomness in molecules also increases. This increase in randomness will result in increase in viscosity as viscosity of gas depends on randomness & collision of gas molecules.

Phenomenon: As a gas is heated, the movement of gas molecules increases and the probability that one gas molecule will collide with another gas molecule increases. In other words, increasing gas temperature causes the gas molecules to collide more often. This increases the gas viscosity because the transfer of momentum between stationary and moving molecules is what causes gas viscosity.

At base P_B = 750 mm of Hg

At top, P_A = 600 mm of Hg

∴ Pressure difference = 150 mm of Hg

(ΔP) = hρg

⇒ Height of mountain = 2040 m

The runaway speed of a water turbine is its speed at full flow, and no shaft load. The turbine will be designed to survive the mechanical forces of this speed.

Centre of Pressure on a Immersed surface from water surface is given by:

For vertical surface θ = 90°

So, the formula is valid for θ = 90°

The flow is defined as uniform flow when in the flow field the velocity and other hydrodynamic parameters do not change from point to point at any instant of time. For a uniform flow, there will be no spatial distribution of hydrodynamic and other parameters.

When the velocity and other hydrodynamic parameters changes from one point to another the flow is defined as non-uniform.

A steady flow is defined as a flow in which the various hydrodynamic parameters and fluid properties at any point do not change with time.

One-dimensional flow is the flow where all the flow parameters may be expressed as functions of time and one space coordinate only. The single space coordinate is usually the distance measured along the centre-line (not necessarily straight) in which the fluid is flowing. Example: the flow in a pipe is considered one - dimensional when variations of pressure and velocity occur along the length of the pipe, but any variation over the cross-section is assumed negligible.

Turbulent fluid motion can be considered as an irregular condition of flow in which various quantities (such as velocity components and pressure) show a random variation with time and space.

The separation point S is determined from the condition

⇒ Flow will not separate.

Kaplan turbine has adjustable runner blades. Kaplan Turbine has very small number of blades 3 to 8. France Turbine has very large number of blades 16 to 24

Equation of stream line is given as

⇒ Vdx – udy = 0

Dynamic viscosity of gases increase with temp μ∝T−−√μ∝T

Density of gases decreases with increase in temp ρ∝

T₁ = 20 + 273 = 293 K   T₂ = 70 + 273 = 343 K
ν₁ = 1.6 × 10^-5 m²/s       ν₂ = ?

PdA - (P + dP) dA - ρgdAds sin θ = 0

⇒dPρ+VdV+gdz=0⇒dPρ+VdV+gdz=0

Assumptions in Bernoulli’s equation:

i) fluid is ideal

ii) flow is steady

iii) flow is continuous

iv) fluid is incompressible

v) flow is non-viscous

vi) flow is irrotational

vii) applicable along a stream line

where,

• The line representing the sum of all 3 head is known as total energy line or total head line
• Line joining the points of piezometric heads is known as hydraulic grade line or piezometric line.

An ideal fluid is a fluid that has several properties including the fact that it is:

Incompressible - the density is constant with respect to pressure.

Irrotational - the flow is smooth, no turbulence.

Nonviscous - (Inviscid) fluid has no internal friction (η = 0)

For soap bubble

∴ Diameter = 40 mm

If the expression is  then it has units of total energy per unit volume.

The expression  , has units of energy per unit weight.

Viscosity is the property of the fluid to resist the rate at which deformation takes place when the fluid is acted upon by shear force

A fluid when acted upon by a shear stress will deform when the applied shear stress is greater than the viscous strength of the fluid.