Test: Fluid Mechanics- 1

The conditions to be satisfied for the applicability of Bernoulli’s equation are

I. Flow along a stream line

II. Flow is steady and Incompressible

III. Effect of viscous forces is negligible

For the pipe of constant diameter, the hydraulic gradient line is always sloping down in the direction of flow and is parallel to total energy line and the difference between both the lines represents velocity head. Due to h_f(head loss due to friction) along the length of pipe, H.G.L always sloping down.

When the flow conditions changes form super critical (F_r > 1) to subcritical (F_r < 1), this results to an abrupt rise of water accompanied by turbulent rollers is called as hydraulic Jump or standing wave.

The hydraulic Jump occurs when the grade changes from sleep to mild

Coefficient of velocity through orifice =ActualvelocityTheoreticalvelocity

V_theo > V_act

So, C_v is always less than 1.

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°

Mechanical efficiency of Impulse turbine is given by:

It generally varies between 97 to 99

Also, volumetric efficiency (η_v) = 97 to 99

Overall efficiency (η_o) = 85 to 90

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.

200 kPa = 200,000 Pa

200,000 Pa = 200,000 N/m²

Pressure in liquids is calculate by the formula:

P = αgh

Where P = pressure, α = density, g = force of gravity,  and h = height

Taking g = 10

αgh = 200,000

1590 x 10 x h = 200,000

h = 200,000/15900

h = 12.58 m

θ = 90°

A = 1 × 4.5 m²

h¯CP= 4.2 metre

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

u = - 2x

V = 2y

For continuity to be satisfied

-2 + 2 = 0

(Hence satisfied)

For a given discharge Q in a channel, there will be two depths for a given specific energy. These two depths are known as alternate depths.

Viscous forces and pressure forces are responsible for drag forces. There are two types of drag forces present pressure drag and skin friction drag. Pressure drag is due to the wake region behind the body and skin friction drag is due to the viscosity of the fluid.

In case of flow over a thin plate placed parallel to a stream of flowing fluid, the flow separation (if occurs), would occur only towards the rear end and the wake is negligibly small. The resulting pressure drag will also be very small, approximate to zero.

On the other hand, pressure drag will be large when the thin plate is held perpendicular to the flow.

Pumps in Parallel:

Same Head: H = H₁ = H₂

Add the discharge: Q = Q₁ + Q₂

Pumps in Series:

Same Discharge: Q = Q₁ = Q₂

Add the heads: H = H₁ + H₂

In thermodynamics an isentropic process is an idealized thermodynamic process. that is both adiabatic and reversible. The work transfer of system is friction-less and there is no transfer of heat as matter.

Manometric head is the head against which head is required to be produced by the pump to deliver water to the destination. Manometric head is higher than the sum of suction and delivery heads because it accounts for head losses due to friction.

Flow separation occurs when the pressure gradient is positive and velocity gradient is negative.

D = depth of flow

d = diameter of pipe

R_m = Hydraulic Mean depth = A/P

Perimeter, P = αd

Condition for Maximum Discharge for Circular Section:

α = 154° = 2.65 radians

D = 0.95 d

R_m = 0.29 d

Condition for Maximum Velocity for Circular Section:

α = 128.75° = 2.25 radians

D = 0.81 d

R_m = 0.3 d

The device used for measurement of viscosity is known as viscometer. According to Saybolt viscometer:

Power required:

A stream lined body is defined as the body whose surface coincides with the stream - lines, when the body is placed in a flow. In that case the separation of flow will take place only at trailing edge (or rearmost part of the body).

Behind a stream lined body, wake formation zone will be very small and consequently the pressure drag will be very small. Thus the total drag on the stream lined body will be due to friction (shear) only.