Introduction to Hydraulics PDF

Introduction to Hydraulics CHAPTER ONE Hydraulics is a topic in applied science and engineering dealing with the mechanical properties of liquids or fluids. At a very basic level, hydraulics is the liquid version of pneumatics. Fluid mechanics provides the theoretical foundation for hydraulics, whic...

Introduction to Hydraulics CHAPTER ONE Hydraulics is a topic in applied science and engineering dealing with the mechanical properties of liquids or fluids. At a very basic level, hydraulics is the liquid version of pneumatics. Fluid mechanics provides the theoretical foundation for hydraulics, which focuses on the engineering uses of fluid properties. Engineering hydraulics is concerned broadly with civil engineering problems in which the flow or management of fluids, primarily water, plays a role. Solutions to this wide range of problems require and understanding of the fundamental principles of fluid mechanics in general and hydraulics in particular and these are summarized in this section. 1.2 Matter Matter is recognized in nature as solid, liquid or gas (or vapour). When it exists in liquid or gaseous form, matter is known as a fluid. The common property of all fluids is that they must be bounded by impermeable walls in order to remain in an initial shape. If the restraining walls are removed the fluid flows expands until a new set of impermeable boundaries is encountered. Provided there is enough fluid or it is expandable enough to fill the volume bounded by a set of impermeable walls, it always conforms to the geometrical shape of the boundaries. In other words, a fluid by itself offers no lasting resistance to change of shape. Hence the fluid can be defined as a substance which readily changes its shape under the action of very small forces. 1.3 The Viscous Flow This is a type of fluid flow in which there is a continuous steady motion of the particles, the motion at a fixed point always remaining constant. The viscosity is that property of a fluid which by virtue of cohesion and interaction between fluid molecules offers resistance to shear deformation. Different fluid deform at different rates under the action of the same shear stress. A liquid's viscosity depends on the size and shape of its particles and the attractions between them. For example, honey has a much higher viscosity than water. A liquid's viscosity depends on the size and shape of its particles and the attractions between them. For example, honey has a much higher viscosity than water. A fluid that has no resistance to shear stress is known as an ideal fluid or inviscid fluid. Zero viscosity is observed only at very low temperatures, in super fluids. Otherwise, all fluids have positive viscosity. If the viscosity is very high, for instance in pitch, the fluid will appear to be a solid in the short term. A liquid whose viscosity is less than that of water 4 5 is sometimes known as a mobile liquid, while a substance with a viscosity substantially greater than water is called a viscous liquid. 1.4 Pressure Drop Pressure drop is defined as the difference in pressure between two points of a fluid carrying network. Pressure drop occurs when frictional forces, caused by the resistance to flow, act on a fluid as it flows through the tube. The main determinants of resistance to fluid flow are fluid velocity through the pipe and fluid viscosity. Pressure drop increases proportional to the frictional shear forces within the piping network. A piping network containing a high relative roughness rating as well as many pipe fittings and joints, tube convergence, divergence, turns, surface roughness and other physical properties will affect the pressure drop. High flow velocities and / or high fluid viscosities result in a larger pressure drop across a section of pipe or a valve or elbow. Low velocity will result in lower or no pressure drop. 1.4.1 Causes of Pressure drop in pipes Friction Vertical pipe difference or elevation Changes of kinetic energy 1.4.2 Determination of the fluid (liquid or gas) pressure drop along a pipe or pipe component Determine the Pressure drop in circular pipes by using the equation: L = Length of Pipe D = Pipe Diameter = Density; v= Flow Velocity If you have valves, elbows and other elements along your pipe then it is possible to calculate the pressure drop with resistance coefficients specifically for the element. The resistance coefficients are in most cases found through practical tests and through vendor specification documents. If the resistance coefficient is known, then we can calculate the pressure drop for the element. 6 Drop; ρ = density; v=Flow Velocity =Coefficient (determined by test or vendor’s specification) 1.4.3 Pressure drop by gravity or vertical elevation The expression for pressure drop by gravity of elevation is as written as : Where: Drop; = Density; g = Acceleration of Gravity, 1.4.4 Pressure drop in gasses and vapor Compressible fluids expansion caused by pressure drops (friction) lead to the velocity increase. Therefore, the pressure drop along the pipe is not constant. The mathematical expression used to estimate the pressure drop is as written as: where: p1 = Pressure incoming; T1 = Temperature incoming, ρ = density p2 = Pressure leaving; T2 = Temperature leaving We set the pipe friction number as a constant and calculate it with the input-data. The temperature, which is used in the equation, is the average of entrance and exit of pipe. 1.5 A shear stress A shear stress, denoted as (Greek: tau), is defined as the component of stress coplanar with a material cross section. Shear stress arises from the force vector component parallel to the cross section. Normal stress, on the other hand, arises from the force vector component perpendicular to the material cross section on which it acts. 7 1.5.1 General shear stress The formula to calculate average shear stress is force per unit area. where: F = the force applied; A=the cross- sectional area of material with area parallel to the applied force vector 1.5.2 Shear Stress (fluid) Shear Stress ( ) is a measure of the force of friction from a fluid acting on a body in the path of that fluid. In the case of open channel flow, it is the force of moving water against the bed of the channel. Shear stress is calculated as: Where: τ = Shear Stress ( ); ɣ = Unit Weight of Water ) D = Average water depth (m); S Sw = Water Surface slope (m/m) 1.5.3 Shear stress in term of velocity gradient The equation relating to the shear stress with velocity gradient is as written as follows: Where: = shear stress ( ); = velocity gradient or rate of deformation = the coefficient of dynamic (or absolute) viscosity ( or kg/ms) 1.6 Dynamic viscosity and Kinematic viscosity Dynamic viscosity is the constant in shear stress in term of velocity gradient, while the ratio of dynamic viscosity to density is known as kinematic viscosity. 8 Where: = Kinematic viscosity ( ); = Density ( ); = Dynamic viscosity ( or kg/ms) 1.7 Compressibility and Bulk modulus Compressibility is measured as the change in volume of a substance due to a change in the pressure applied on it, while Bulk modulus of material is defined as change in pressure per volume strain. Mathematically (a) where p = pressure; V= volume Also density But for a unit mass of fluid, the density or (b) Substituting (b) into (a) gives (c) Equation ( c ) is the compressibility of the fluid and K has the unit of pressure i.e ( ). 1.8 Reynolds Number Reynolds Number is the ratio of the inertial forces to the viscous forces and it is a dimensionless quantity. In the 19th century, Osborne Reynolds, an English scientist working at the University of Manchester demonstrated through experiment that the flow of a liquid through a pipe is essentially of two types. These are : (a) Laminar flow and (b) Turbulent flow The intermediary flow between (a) and (b) is refers to as Transitional flow. He classified fluid flow into the above categories based on the ratio of inertial force to viscous force acting on particles within such flow. This ratio is known as Reynolds number denoted by Re. where ρ= density; v= flow velocity; L= characteristic length such as the pipe diameter (D) = the coefficient of dynamic (or absolute) viscosity ( or kg/ms) The flow of fluid in a pipe and open channel can then be categories as follows: Type of flows Pipes Laminar flow Open channels Re < 2000 Transitional flow Re < 500 Re 2000 ≤Re≤ 4000 Turbulent flow 500 ≤Re≤ 2000 Re > 4000 Re > 2000 Laminar flow is characterized by the gliding of concentric cylindrical layers past one another in orderly fashion. The velocity of the fluid is at its maximum at the pipe axis and decreases sharply to zero at the wall. The pressure drop caused by friction of laminar flow does not depend on the roughness of pipe. Turbulent flow: There is an irregular motion of fluid particles in directions transverse to the direction of the main flow. The velocity distribution of turbulent flow is more uniform across the pipe diameter than in laminar flow. 9 1.8.1 Physical significance of Reynolds Number: 1. It signifies the relative predominance of inertia to viscous forces. 2. It is very useful in determining whether the flow is laminar or turbulent. 3. Require to determine friction coefficient of pipe & roughness coefficient of channel 1.8.2 Use of Reynolds (Re) number in Selection of pipe friction Coefficient: The pipe friction coefficient is a dimensionless number. The friction factor for laminar flow condition is a function of Reynolds number only, for turbulent flow it is also a function of the characteristics of the pipe wall. (a) Determine Pipe friction coefficient at laminar flow: Pipe Friction Coefficient; Re = Reynolds number Note: Perfectly smooth pipes will have a roughness of zero. (b) Determine Pipe friction coefficient at turbulent flow (in the most cases): = Pipe Friction Coefficient; Re = Reynolds Number k = Absolute Roughness; D = Diameter of Pipe Practice Questions 1. Two horizontal plates are placed 1.25 cm apart, the space between them being filled with oil of viscosity 14 poise (1.4 Ns/m2). Compute the shear in the oil if the upper plate is moved with a velocity of 4 m/s. 2. (i) Differentiate between Compressibility and Bulk Modulus of a Fluid (ii) List three (3) Physical significance of Reynolds Number 3. Glycerine of viscosity 0.9Ns/m2 and desisity 1260kg/m3 is pumped along a horizontal pipe 6.5m long of diameter d=0.01m at a flow rate of Q=1.8 litres/min. Determine the flow Reynolds number and verify whether the flow is laminar or turbulent. Calculate the pressure loss in the pipe due to frictional effects.