nce403 mod unit4

Classical hydraulic jump, Evaluation of the jump elements in rectangular and

nonrectangular channels on horizontal and sloping beds. Rotodynamic pumps, classification on different basis, basic

equations, Velocity triangles, manometric head, efficiencies, cavitation in pumps, characteristics curves.

05/02/23 1MODASSAR ANSARI

BY MODASSAR ANSARI 2nd Year Department of civil Engineering SUBJECT- HYDRAULICS & HYDRAULIC

MACHINES SUBJECT CODE-NCE 403


A hydraulic jump is formed when flow changes from supercritical to subcritical flow.

In this transition from the supercritical to subcritical flow, water surface rises abruptly, surface rollers are formed, intense mixing occurs, air is entrained, and usually a large amount of energy is dissipated.

By utilizing these characteristics, a hydraulic jump may be used to dissipate energy, to mix chemicals, or to act as an aeration device.


A rotodynamic pump is a device where mechanical energy is transferred from the rotor to the fluid by the principle of fluid motion through it. The energy of the fluid can be sensed from the pressur and velocity of the fluid at the delivery end of the pump. Therefore, it is essentially a turbine in reverse. Like turbines, pumps are classified according to the main direction of fluid path through them like (i) radial flow or centrifugal, (ii) axial flow and (iii) mixed flow types.


The basic equation of fluid dynamics relating to energy transfer is same for all rotodynamic machines and is a simple form of " Newton 's Laws of Motion" applied to a fluid element traversing a rotor. Here we shall make use of the momentum theorem as applicable to a fluid element while flowing through fixed and moving vanes


Figure 4.2 represents diagrammatically a rotor of a generalized fluid machine, with 0-0 the axis of rotation and the angular velocity. Fluid enters the rotor at 1, passes through the rotor by any path and is discharged at 2. The points 1 and 2 are at radii r1 and r2 from the centre of the rotor, and the directions of fluid velocities at 1 and 2 may be at any arbitrary angles.


The flow is steady, that is, the mass flow rate is constant across any section (no storage or depletion of fluid mass in the rotor).

The heat and work interactions between the rotor and its surroundings take place at a constant rate.

Velocity is uniform over any area normal to the flow. This means that the velocity vector at any point is representative of the total flow over a finite area. This condition also implies that there is no leakage loss and the entire fluid is undergoing the same process.


However, for an axisymmetric flow, this does not result in any net radial force on the rotor. In case of a non uniform flow distribution over the periphery of the rotor in practice, a change in momentum in radial direction may result in a net radial force which is carried as a journal load. The tangential component Vw only has an effect on the angular motion of the rotor. In consideration of the entire fluid body within the rotor as a control volume, we can write from the moment of momentum theorem.


05/02/23

from the moment of momentum theorem

where T is the torque exerted by the rotor on the moving fluid, m is the mass flow rate of fluid through the rotor. The subscripts 1 and 2 denote values at inlet and outlet of the rotor respectively

11MODASSAR ANSARI

The rate of energy transfer to the fluid is then given by

where ω is the angular velocity of the rotor and U= ωr which represents the linear velocity of the rotor. Therefore U1 and U1 are the linear velocities of the rotor at points 2 (outlet ) and 1 (inlet) respectively (Fig. 4.2). The above is known as Euler's equation in relation to fluid machines. The Eq. can be written in terms of head gained 'H' by the fluid as


The pumps employing centrifugal effects for increasing fluid pressure have been in use for more than a century. The centrifugal pump, by its principle, is converse of the Francis turbine. The flow is radially outward, and the hence the fluid gains in centrifugal head while flowing through it. Because of certain inherent advantages, such as compactness, smooth and uniform flow, low initial cost and high efficiency even at low heads, centrifugal pumps are used in almost all pumping systems. However, before considering the operation of a pump in detail, a general pumping system is discussed as follows.


The ratio of manometric head H and the work head imparted by the rotor on the fluid (usually known as Euler head) is termed as manometric efficiency . It represents the effectiveness of the pump in increasing the total energy of the fluid from the energy given to it by the impeller. Therefore, we can write


The overall efficiency of a pump is defined as

where, Q is the volume flow rate of the fluid through the

pump, and P is the shaft power, i.e. the input power to the shaft.


Thus a mechanical efficiency is defined as

So that,


Elementary analysis of axial turbines too begins with velocity triangles.

The analysis will be carried out at the mean height of the blade, where the peripheral velocity or the blade speed is, U.

The absolute component of velocity will be denoted by, C and the relative component by, V.

The axial velocity (absolute) will be denoted by Ca and the tangential components will be denoted by subscript w (for eg, Cw or Vw)

α denotes the angle between the absolute velocity with the axial direction and β the corresponding angle for the relative velocity.


Cavitation is likely to occur at the inlet to the pump, since the pressure there is the minimum and is lower than the atmospheric pressure by an amount that equals the vertical height above which the pump is situated from the supply reservoir (known as sump) plus the velocity head and frictional losses in the suction pipe. Applying the Bernoulli's equation between the surface of the liquid in the sump and the entry to the impeller, we have


where, Pi is the pressure at the impeller inlet and PA is the pressure at the liquid surface in the sump which is usually the atmospheric pressure, z is the vertical height of the impeller inlet from the liquid surface in the sump, hf is the loss of head in the suction pipe.


The pump characteristic curves can be defined as ‘the graphical representation of a particular pump’s behavior and performance under different operating conditions’.

The operating properties of a pump are established by the geometry and dimensions of the pump’s impeller and casing. Curves relating total head, efficiency, power, and net positive suction head required (NPSHR) to discharge or pump capacity (Q) are utilized to describe the operating properties (characteristics) of a pump. This set of four curves is known as the pump characteristic curves or pump performance curves.
