The equation of continuity

Considering that

1. penetration of fluid through the side surface is impossible (because the surface is formed by current lines)

2. The liquid is incompressible

3. The liquid is a continuous medium (there are no discontinuities) can be written

u₁d w ₁dt = u₂d w ₂dt Q = const

u₁/u₂ = d w ₂/d w ₁ v₁/v₂ = w ₂ / w ₁

Differential equations of motion of an ideal fluid

When studying the motion of a liquid, it is necessary to consider a number of quantities that were absent in the study of a liquid at rest. This projection of the acceleration of the volume forces, the projection of velocity, hydrodynamic pressure and density. The main task of hydrodynamics is to establish the dependence of these variables on the coordinates and time.

Previously, differential equations of fluid equilibrium were obtained. In order to pass from them to the equations of motion according to the D'Alambert principle, it is necessary to add inertia forces. For an elementary parallelepiped, the projection of the inertia force on the X axis will be r dx dy dz du_x/dt, i.e. product of mass by acceleration. Equilibrium equations were written in terms of unit mass forces, so the equations of motion can be represented as follows.

These equations are called the Euler equations, as well as the equations of dynamic equilibrium.

These equations are valid for an ideal fluid. When considering a real fluid, it is necessary to add viscosity forces. The system of equations obtained in this way is called the Navier-Stokes equations.

 

CONTROL QUESTIONS

1. What is the steady and unsteady movement?

2. What fluid motion is called uniform and uneven?

3. What kind of fluid motion is called pressure and non-pressure?

4. What is called an elementary trickle, and what properties it is characterized by?

5. What is called a fluid flow?

6. What steady motion is called smoothly changing, and what properties is it characterized by?

7. What is a live flow cross-section, wetted perimeter and hydraulic radius?

8. What is called the flow rate and the average fluid flow rate?

9. Formulate and write down the continuity equation for the fluid flow?

 

 

MEASUREMENT OF FLOW

VOLUME-type flowmeters.

To account for the amount of liquid consumed by individual small consumers (residential and public buildings, small businesses, individual shops), mechanical speed water meters are the most widely used.

According to the design, high-speed (tachometric) liquid counters are divided into two main groups: winged, whose axis of rotation is perpendicular to the direction of movement of the fluid, and turbine, in which the axis of rotation of the turbine is parallel to the direction of movement of the liquid.

The principle of action of high-speed liquid meters is based on measuring the number of revolutions of the impeller or impeller, driven by the flow of liquid flowing through the counter. The speed of the impeller or impeller is proportional to the amount of liquid flowing through the counter. The axis of the impeller or turbine is connected to the counting mechanism by means of a transmission mechanism, which, taking into account the number of revolutions, shows the amount of liquid flowing through the counter.

Qmax is the maximum flow rate at which the meter can work for a short time, no more than one hour per day;

Qnom is the nominal flow rate at which the meter can run for a long time;

Qo is the operating flow rate at which the meter can operate continuously throughout the life of the device;

Qmin - the lowest consumption, for which the limit of the permissible relative error is normalized;

Qth.s. - threshold of sensitivity, such a smallest flow rate, at which the steady rotation of the meter working part begins.

 

 

 

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