Prof. Abdullah S. Alghamdi https:/ aghamdi.kau.sa Office: 44C48

1. CE 401 – Civil Engineering Fundamentals - Fall 2019 Prof. Abdullah S. Alghamdihttps:/aghamdi.kau.edu.saOffice: 44C48

2. Suggested References 1.Fundamentals of Hydraulic Engineering Systems. By Ned Hwang & Robert Houghtalen. 2. Hydraulic Engineering. By Roberson, Cassidy & Chaudary. 3. FE Civil Review Manual by Michael R. Lindeburg PE

3. Mass (Density) and Weight (Specific Weight) • The density of a substance: is defined as mass per unit volume. r = m/Vol • The density of water is a function of Temperature • Water maximum densityreaches a maximum density at 4°C. • Density of sea water,because sea water contains salt, the density about 4% more than that of fresh water.

4. In the S.I. system the weight of an object is defined by the product of its mass (m, in grams, kilograms, etc.), and the gravitational acceleration (g = 9.81 m/sec2 on earth). W=m*g • Weight is expressed in the force units of newton (N). (One newton is defined as the force required to accelerate 1 kg of mass at a rate of 1 m/sec2). • The specific weight (g)=(weight per unit volume) of water, g = r g. The specific weight of water is a function of T (see Table 1.2). • Specific gravity (S) the ratio of the specific weight of any liquid to that of water at 4°C.

7. Viscosity of Water • Consider that water fills the space between two parallel platesat a distance y apart. A horizontal force Tis applied to the upper plate and moves it to the right at velocity Vwhile the lower plate remains stationary. The shear force T is applied to overcome the water resistance R, and it must be equal to Rbecause there is no acceleration involved in the process.

8. Figure 1.1 Shearing stresses in fluids Viscosity of Water

9. Viscosity of Water • The resistance per unit area of the upper plate, shear stress, is proportional to the rate of angular deformation in the fluid, d(q)ldt. • a d(q)ldt • = constant (dx/dy)/dt • = µ(dx/dt)/dy • = µ dv/dy(Newton's law of viscosity)…………Equation (1.2) The proportionally constant, m., is called the absolute viscosity of the fluid.

10. EXAMPLE If the velocity distribution of a viscous liquid (µ = 0.9 Ns/m2) over a fixed boundary is given by u = 0.68 y – y2 in which ‘u’ is the velocity in m/s at a distance y meters above the boundary surface, determine the shear stress at the surface and at y = 0.34 m.

11. Surface Tension and Capillarity • Even at a small distance below the surface of a liquid body, liquid molecules are attracted to each other by equal forces in all directions. • The molecules on the surface, however, are not able to bond in all directions and therefore form stronger bonds with adjacent water molecules. This causes the liquid surface to seek a minimum possible area by exerting surface tension tangent to the surface over the entire surface area. • A steel needle floating on water, the spherical shape of dewdrops, and the rise or fall of liquid in capillary tubes are the results of surface tension.

12. Figure 1.2 Wetting and nonwetting surfaces

13. Most liquids adhere to solid surfaces. • The adhesive force varies depending on the nature of the liquid and of the solid surface. • If the adhesive force between the liquid and the solid surface is greater than the cohesionin the liquid molecules, the liquid tends to spread over and wet the surface, as shown in Figure 1.3(a). • If the cohesion is greater, a small drop forms, as shown in Figure 1.3(b). • Water wets the surface of glass, but mercury does not. If we place a small bore vertical glass tube into the free surface of water, the water surface in the tube rises (capillary rise ). The same experiment performed with mercury will show that the mercury falls. The phenomenon is commonly known as capillary action

14. Figure 1.3 Capillary actions

15. The magnitude of the capillary rise (or depression), h, is determined by the balance of adhesive force between the liquid and solid surface and the weight of the liquid column above (or below) the liquid-free surface. • The angle (theta) at which the liquid film meets the glass depends on the nature of the liquid and the solid surface. • The upward (or downward) motion in the tube will cease when the vertical component of the surface tension force around the edge of the film equals the weight of the raised (or lowered) liquid column.

16. When the very small volume of liquid above (or below) the base of the curved meniscus is neglected, the relationship may be expressed as • The surface tension of a liquid is usually expressed in the units of force per unit length. Its value depends on the temperature and the electrolytic content of the liquid. Small amounts of salt dissolved in water tend to increase the electrolytic contentand, hence, the surface tension. Organic matter (such as soap) decreases the surface tension in water and permits the formation of bubbles. • The surface tension of pure water is listed in Table 1.4.

17. Table 1.4 Surface Tension of Water

18. Buoyancy Archimedes' principle: • The weight of a submerged body is reduced by an amount equal to the weight of the liquid displaced by the body.

19. Question 5:

21. Water Pressure and Pressure Forces

22. Free Surface of Water • a horizontal surface upon which the pressure is constant everywhere. • free surface of water in a vessel may be subjected to: - the atmospheric pressure (open vessel) or - any other pressure that is exerted in the vessel (closed vessel).

23. Absolute and Gage Pressures • in contact with the earth's atmosphere A water surface is subjected to atmospheric pressure, which is approximately equal to a 10.33-m-high column of water at sea level. • In still water any object located below the water surface is subjected to a pressure greater than the atmospheric pressure (P>Patm).

24. Consider the following prism -the prism is at rest -all forces acting upon it must be in equilibrium in all directions

25. the difference in pressure between any two points in still water is always equal to: the product of the specific weight of water and the difference in elevation between the two points. Fx = PA dA –PB dA + g L dA sin j= PA –PB = g h • If the two points are on the same elevation, h = 0. • In other words, for water at rest, the pressure at all points in a horizontal plane is the same. • If the water body has a free surface that is exposed to atmospheric pressure,Patm.

26. Gage pressure & Absolute pressure • Pressure gages • are usually designed to measure pressures above or below the atmospheric pressure. • Gage pressure, P • is the pressure measured w.r.t atmospheric pressure. • Absolute pressure (measured w.r.t vacuum) • is always equal to: • Pabs = Pgage + Patm • Pressure head, h = P/g

27. the difference in pressure heads at two points in water at rest is always equal to the difference in elevation between the two points. (PB /g) – (PA /g) = D(h) • From this relationship imply that any change in pressure at point B would cause an equal change at point A, because the difference in pressure head between the two points must remain the same value h. • Pascal's law : a pressure applied at any point in a liquid at rest is transmitted equally and undiminished in all directions to every other point in the liquid. This principle has been made use of in the hydraulic jacks that lift heavy weights by applying relatively small forces.

29. Manometers • A manometer: is a tube bent in the form of a U containing a fluid of known specific gravity. The difference in elevations of the liquid surfaces under pressure indicates the difference in pressure at the two ends. • Two types of manometers: • 1. an open manometer has one end open to atmospheric pressure and is capable of measuring the gage pressure in a vessel; (Fig 2.5 a) • 2. a differential manometer connects each end to a different pressure vessel and is capable of measuring the pressure difference between the two vessels. (Fig 2.5b)

32. A simple step-by-step procedure is suggested for pressure computation • Step 1. Make a sketch of the manometer system, similar to that in Figure 2.5, approximately to scale. • Step 2. Draw a horizontal line at the level of the lower surface of the manometer liquid,1. The pressure at points 1 and 2 must be the same since the system is in static equilibrium. • Step 3. (a) For open manometers, the pressure on 2 is exerted by the weight of the liquid M column above 2; and the pressure on 1 is exerted by the weight of the column of water above 1 plus the pressure in vessel A. The pressures must be equal in value.

34. Hydrostatic Force on a Flat Surface • Take an arbitrary area AB on the back face of a dam that inclines at an angle (q ) and then place the x-axis on the line at which the surface of the water intersects with the dam surface, with the y-axis running down the direction of the dam surface.

35. Figure 2.9(a) shows a horizontal view of the area and Figure 2.9(b) shows the projection of AB on the dam surface.

36. the total hydrostatic pressure force on any submerged plane surface =is equal to the product of the surface area and the pressure acting at the centroid of the plane surface. • Pressure forces acting on a plane surface are distributed over every part of the surface. They are parallel and act in a direction normal to the surface. (can be replaced by a single resultant force F of the magnitude shown in Equation (2.12). • The resultant force also acts normal to the surface. The point on the plane surface at which this resultant force acts is known as the center of pressure.

37. The center of pressure of any submerged plane surface is always below the centroid of the surface (i.e., Yp > yc). • The centroid, area, and moment of inertiawith respect to the centroid of certain common geometrical plane surfaces are given in Table 2.1.

41. Hydrostatic Forces on Curved Surfaces • The hydrostatic force on a curved surface can be best analyzed by = resolving the total pressure force on the surface into its horizontal and vertical components. (Remember that hydrostatic pressure acts normal to a submerged surface.) • Figure 2.12 shows a curved wall of a container gate having a unit width normal to the plane of the paper. • Because the water body in the container is stationary, every part of the water body must be in equilibrium or each of the force components must satisfy the equilibrium conditions

43. FA’B Fig 2.12 Hydrostatic pressure on a curved surface

45. Water Flow in Pipes • P ipe flow : • Is a full water flow in closed conduits of circular cross sections under a certain pressure gradient.For a given discharge Q, the pipe flow at any section of the pipe can be described by the pipe cross section: • Q= f(A, Z, P, V) • The elevation of a particular section in the pipe is usually measured with respect to a horizontal reference datum (i.,e. (MSL  mean sea level)

48. Fig 3.5 Energy head and head loss in pipe flow

49. The total energy contained in each unit weight of water that passes through section 1. • The total energy contained in each unit weight of water that passes through section 2 • The energy relationship between the two sections. where (hL) is the head loss between sections 1 and 2.

50. @ 20oC