Hydraulics, Irrigation, Water Resource Engineering and Hydrology: December 2013

GATE, PSUs - Hydraulics, Irrigation, water resource Engg. notes - part 3

Hello there,
How have you been!

Are you preparing yourself for some Engineering exams such as GATE or for PSUs?

A multipurpose reservoir is one that is planned and constructed to serve various multi-purposes.
The useful storage is the volume of water stored in the reservoir between minimum pool level and normal pool level.
The water stored in the reservoir below the the minimum pool level is called dead storage.
For a flood control reservoir, the effective storage is equal to Useful Storage+ Surcharge Storage - Valley Storage.
Trap efficiency of a reservoir is a function of capacity/inflow ratio.
The force considered for the analysis of the elementary profile of gravity dam under empty reservoir conditions is the dam's self-weight.
The uplift pressure on a dam can be controlled by :

constructing cutoff under upstream face
constructing drainage channels between the dam and its foundations
by pressure grouting in the foundation

The uplift pressure on the face of a drainage gallery in a dam is taken as two-third of hydro-static pressure at toe plus one-third of hydro-static pressure at the heel.
Horizontal acceleration due to earth-quake results in hydro-dynamic pressure and inertia force into the body of the dam.
Hydro-dynamic pressure due to earthquake acts at a height of 4H/3.pi. above the base.
The major resisting force in a gravity dam is self-weight.
Total force due to wave action on a gravity dam acts at a height of 3/8*hw above the reservoir surface, where hw = water depth.
When the reservoir is full, maximum compressive force in a gravity dam is produced at the toe.
The maximum permissible eccentricity for no tension at the base of a gravity dam is B/6.
The presence of tailwater in a gravity dam decreases the principal stress and shear stress.
The elementary profile of a dam is a right-angled triangle.
In the empty condition of the reservoir and with the elementary profile of a dam, the vertical stress at heel and toe respectively are given by 2W/B and 0.

References (Also the best books for GATE and PSU preparations):

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GATE, PSUs - Hydraulics notes - part 2

Hello there,

How you have been? Here is a collection of notes for preparation of the GATE and PSU exams.

Super critical flow can occur in a channel with mild slope, channel with a steep slope and also in a horizontal channel.
Analysis of a surge in a open channel is carried out by continuity equation or momentum equation.
Mild slope profile M2 occurs fir depth above critical but below normal.
For a steep slope profile S1, the type of flow will be sub-critical.
A Froude number 1.0 to 1.7 represents an undulant jump, 1.7 to 2.5 a weak jump, 2.5 to 4.5 an oscillatory jump and 4.5 to 9.0 a steady jump.
The height of hydraulic jump is equal to difference in conjugate depths.
If Y1 and Y2 are the conjugate depths before and after the hydraulic jump, then (Y2-Y1)^3/(4.Y1.Y2) gives us the loss of energy in the hydraulic jump.
The value of Froude's number can be less than 1, equal to one or greater than one.
Froude's number is the ratio of inertial force to gravity force.
Reynold's number is the ratio of inertial force to viscous force.
Weber number is the ratio of inertial force to Surface Tension force.
Mach number is the ratio of inertial force to compressive force.

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GATE PSUs preparation - Hydraulics - one liners..

Hello there,
How you doing? Here are one liners which might be helpful for your preparations for the GATE and PSUs exams:

For uniform flow in channel, the total energy line, hydraulic gradient line and bottom of channel are all parallel.
The chezy's co-efficient has the dimensions of L^(1/2) T^(-1).
The depth of flow for maximum velocity in a circular channel section is 0.81 times the diameter.
For maximum discharge in a circular channel section, the ratio of depth of flow to the diameter of channel is 0.938(0.95 approx.)
A triangular channel is most economical when each of its sloping side is inclined to the vertical at 45 degree of angle.
For a trapezoidal section to be most economical its hydraulic radius must be equal to Yc/2.
The critical state of flow through a channel section may be defined as the state of flow at which the discharge is maximum for a given specific force.
For a given specific energy E, the critical depth for a rectangular channel is given by Yc = 2/3E.
For the same specific force, the two depths at which a given discharge can occur are called conjugate depths.
The most common instrument/device for measuring discharges through channels is Venturi-flume.
When the slope of bottom of a channel raises in the direction of flow, it is called adverse slope.

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reference: Civil Engineering Objectives by S P Gupta and S P Gupta

Hydraulics - One Liners

Hello,
Here are few one liners from Hydraulics:

1. Open channel flow is in transitional stage when the Reynolds Number is from 500 to 2000.

2. In Pipe flow the flow is turbulent when the Reynolds Number is greater than 4000.

3. A semi- Circular open channel is the best hydraulic section among a circular, rectangular or square channel.

4. When the time of closure for a pressure moving with velocity v for a length of L is less than 2L/v, it is known as rapid closure.

4. A shooting flow is a steady and non-uniform flow.

5. Vena-contracta is the section having smallest cross section of the free flow from an orifice.

6. Co-efficient of discharge Cd= (Co-efficient of velocity)^2 * Co-efficient of contraction.

7. An equivalent pipe is a pipe which has same head loss and discharge as that of the original pipe.

8. If the hydraulic line at a junction is higher than the hydraulic lines at the Reservoir A and B and is lower than that at the reservoir C then, the water will flow from reservoir C to A and B.

9. The difference between two adjacent stream line functions at a section gives us the discharge per unit length.

10. Partial derivative of a stream line function w.r.t. the x and y will give us the velocities in the x and y direction at that point.

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Pilot Tube, Venturimeter and Orificemeter

Hello,

Pilot Tube: Pilot tube is composed of a circular sectioned tube which has a L-shaped longitudinal profile. The two ends of this L-shaped tube are open.

Pilot tube is used to determine the velocity of flow of a fluid. The method is to put one end of the tube parallel to the flow of the fluid and when the stagnation point is reached, we measure the stagnation pressure.

Pilot Tube image source: wikipedia

Theory behind the pilot tube is

stagnation pressure = static pressure + dynamic pressure

Venturimeter: This instrument is used to determine the discharge(Q) of the flow of the fluid.

Orificementer: This instrument is also used to determine the discharge(Q) of the flow of the fluid.

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Boundary Layer Theory of Fluid Flow

Hii,

In fluid dynamics we have to study this theory given by Ludwig Prandtl, known as Boundary Layer Theory.

Boundary Layer Theory:

When a fluid flowing with laminar flow through an infinite thickness with an uniform velocity of U, passes through a boundary which can be the surface of a tube or any bed or wall, the velocity of the the fluid particles near to the boundary is obstructed by the frictional force of the surface and the adhesion of the particle to the surface.

Now these obstructed particles having almost zero velocity are attracting the nearby particles due to the cohesive force known as the viscosity. So the velocity of the particles of the next layers is also retarded.

This way the velocity of the flow changes from the U at the boundary to zero and it increases gradually as we go to the next layer away from the boundary layer.
This increase is almost parabolic in nature and after a certain distance from the boundary layer the flow again gains its uniform velocity U.

Boundary Layers - Laminar and Turbulent Boundary Layers (Source: Wikipedia.org)

This distance at a section depends upon the distance of the section from the starting point of the boundary flow. At the starting point of the boundary flow, the velocity of all the layers is U, but as we go to the further sections, the velocity will decrease near to the boundary layer and gradually increases to its initial value of U at a thickness of 'd'. This 'd' goes on increase with the increase in the distance of the section from the starting point of the boundary section.

Remember:

If the velocity is increased the value of 'd' decreases.
If viscosity is increased the value of 'd' increases.
If upstream pressure is increased, the value of 'd' increases
When Reynold's number R< 2 00 the flow in the boundary layer is laminar and the boundary layer is parabolic and if R > 4 * 10^5 then the boundary layer is turbulent.

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Fluid Kinematics - Types of Flow

Fluid Kinematics:
This is the basic study in the hydraulic engineering along with hydro-statics. Fluid dynamics deals with the study of flow of fluids, while hydro-statics deals with the study of the fluids under flow.
If F is the flow property like, velocity, density etc., of a fluid then we can classify the fluid in the following ways.
(1) Steady and un-steady flow:

Steady Flow: This flow can be defined using the following equation:
Curly(F)/ Curly(t) = 0
Here Curly is used to denote the partial differentiation of the flow property with respect to time at a point or section.
So velocity of the particle is same as the velocity of the previous particle at the section.

Un-Steady Flow:
In this type of flow the flow property changes with time so,
Curly(F)/ Curly(t) =/ 0,
That means velocity, or density etc. of a particle will be different from that of the previous particles at the same section.

(2) Uniform and non-uniform flow:

Uniform Flow: Uniform flow can be defined with the following equation:
dF/dS = 0 ---eq(1)
Here F is the fluid property and S is the flow field. Properties like velocity and density will not change from one point to the other point in the flow field. This equation represents the uniform flow.
Non-uniform flow: Non-uniform flow is the flow in which the the above equation[eq(1)] is not satisfied, so the fluid property changes from one point to another point in the flow field.

(3) Rotational and Ir-rotational Flow:

Ir-rotational Flow: In this type of flow the rotation of the fluid particles about a axis perpendicular to the plane of flow of particle is zero. i.e.
du/dz= dv/dx = dw/dy etc. --- eq(2)

Rotational Flow: This is the flow in which the rotation of the fluid particle about their mass axis which is perpendicular to the plane of flow is not zero. So the above equations[eq(2)] are not satisfied by the rotational flow.

Two very important laws from Hydrostatic

Hi,
Understanding hydro-statics can be easy if you understand the basic laws. The following two laws are very important to understand the further concepts in this study of static fluid:
(1) Pascal's Law
(2) Archimedes Principle

(1) Pascal's Law:
This law states that the magnitude of pressure in a fluid is same/constant in all direction at an area, when area tends to zero.
This law is used in the hydraulic jack, which can lift up heavy automobiles. When small force is applies on a small area, can be transformed to larger force using this principle.
Force on a vertical immersed slit of area A, whose center of gravity is at a height of Hg can be calculated numerically as below.
F = d. Hg. A
where d is the density of the fluid.
This pressure force acts at the center of pressure on the body, which is located at a distance, as given numerically below
H p = Ig/ A.Hg + Hg
where,
Ig = moment of Inertia of the body about its center of gravity.
From the above equation it can be stated that the center of pressure is always below the center of gravity and it co-incides with it when the depth i.e. Hg tends to infinity.

(2) Archimedes Principle:
This law states that when a body is immersed in a liquid, partially or fully, it loses its weight equal to the weight of the liquid displaced by the body. This weight is lost due to the upward force applied by the fluid through the center of buoyancy.
Center of buoyancy is the point same as the center of the gravity of the displaced liquid.
This principle is very very important to manufacture/design the ships.

Thanks.

Hydrostatic law for pressure

This law states that for a static water, the variation of the pressure along the vertical downwards direction is equal to the specific weight of the liquid.
So if 'd' is the specific weight of the liquid, and h is the depth measured from the top surface of the liquid,
then pressure at a point at depth 'd' can be calculated as below

p = d.h (where 'd' is the water density, and 'h' is the depth)

This shows that static pressure at the top surface,
h = 0 , p = 0
and it is maximum when h =H (H is the total depth of the water)
p = d.H
So, this shows the linear variation of the static pressure from top surface to the bottom face.
This can be shown diagrammatically as shown in figure above.