Subject Name FLUID MECHANICS Subject Code 10 ME

Subject Name: FLUID MECHANICS Subject Code: 10 ME 36 B Prepared By: PUNITH R Department: AE Date: 05 -09 -2014

Venturimeter is a device used for measuring the rate of flow of a fluid flowing through a pipe. It consists of three parts: • A short converging part • Throat • Diverging part

Discharge through venturimeter is given by Actual discharge through venturimeter is given by • Actual discharge is always less than theorotical discharge • Coefficient of discharge is always less than 1

Orifice meter: is a device used for measuring the rate of flow of a fluid flowing through a pipe. .

• It is a cheaper device as compared to venturimeter. This also work on the same principle as that of venturimeter. • It consists of flat circular plate which has a circular hole, in concentric with the pipe. This is called orifice. • The diameter of orifice is generally 0. 5 times the diameter of the pipe (D), although it may vary from 0. 4 to 0. 8 times the pipe diameter.

coefficient of discharge of the orifice meter The coefficient of discharge of the orifice meter is much smaller than that of a venturimeter.

Pitot-tube is a device used for measuring the velocity of flow at any point in a pipe or a channel. Principle If the velocity at any point decreases, the pressure at that point increases due to the conservation of the kinetic energy into pressure energy. In simplest form, the pitot tube consists of a glass tube, bent at right angles in pipe

Fig: Pitot-tube Where, p 1 = pressure at section 1 p 2 = pressure at section 2 v 1 = velocity at section 1 H = depth of tube in the liquid h = rise of liquid in the tube above the free surface v 2 = velocity at section 2 = 0

Theorotical and actual velocity Theorotical velocity is given by Actual velocity is given by

Dimensional analysis It is a mathematical technique which makes use of study of dynamics as an art to the solution of engineering problems. Fundamental Dimensions All physical quantities are measured by comparison which is made with respect to a fixed value. Length, Mass and Time are three fixed dimensions. In compressible flow problems, temperature is also considered as a fundamental dimensions. Secondary Quantities or Derived Quantities Secondary quantities are derived quantities or quantities which can be expressed in terms of two or more fundamental quantities.

Dimensional Homogeneity In an equation if each and every term or unit has same dimensions, then it is said to have Dimensional Homogeneity. V = u + at m/s m/s 2 ⋅ s LT-1 = (LT-1) + (LT-2) (T) Uses of Dimensional Analysis 1. It is used to test the dimensional homogeneity of any derived equation. 2. It is used to derive equation. 3. Dimensional analysis helps in planning model tests.

Methods of Dimensional Analysis There are two methods of dimensional analysis. 1. Rayleigh’s method 2. Buckingham’s (Π – theorem) method Rayleigh’s method of analysis is adopted when number of parameter or variables are less (3 or 4 or 5).

Methodology Dimensions for quantities on left hand side as well as on the right hand side are written and using the concept of Dimensional Homogeneity a, b, c …. can be determined.

Buckingham’s Π Method This method of analysis is used when number of variables are more. Buckingham’s Π Theorem If there are n – variables in a physical phenomenon and those n -variables contain ‘m’ dimensions, then the variables can be arranged into (n-m) dimensionless groups called Π terms.

Selecting Repeating Variables 1. Avoid taking the quantity required as the repeating variable. 2. Repeating variables put together should not form dimensionless group. 3. No two repeating variables should have same dimensions. Repeating variables can be selected from each of the following properties: a. Geometric property : Length, height, width, area b. Flow property : Velocity, Acceleration, Discharge c. Fluid property : Mass density, Viscosity, Surface tension

Model analysis Before constructing or manufacturing hydraulics structures or hydraulics machines tests are performed on their models to obtain desired information about their performance. Models are small scale replica of actual structure or machine. The actual structure is called prototype. Similitude / Similarity It is defined as the similarity between the prototype and it’s model. Types of Similarity There are three types of similarity. o Geometric similarity o Kinematic similarity o Dynamic similarity

Geometrical Similarity Geometric similarity is said to exist between the model and prototype if the ratio of corresponding linear dimensions between model and prototype are equal.

Kinematic Similarity Kinematic similarity exists between prototype and model if quantities such at velocity and acceleration at corresponding points on model and prototype are same.

Dynamic Similarity Dynamic similarity is said to exist between model and prototype if ratio of forces at corresponding points of model and prototype is constant.

Dimensionless Numbers Following dimensionless numbers are used in fluid mechanics. 1. Reynold’s number 2. Froude’s number 3. Euler’s number 4. Weber’s number 5. Mach number