Fluid Mechanics61341


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1 AnNajah National University College of Engineering Fluid Mechanics Chapter [5] Flow of An Incompressible Fluid Dr. Sameer Shadeed 1 Fluid Mechanics2nd Semester [5] Flow of An Incompressible Fluid Dr. Sameer Shadeed
2 Euler s Equation 2 Fluid Mechanics2nd Semester [5] Flow of An Incompressible Fluid Dr. Sameer Shadeed
3 Euler s Equation 3 Fluid Mechanics2nd Semester [5] Flow of An Incompressible Fluid Dr. Sameer Shadeed
4 Euler s Equation 4 Fluid Mechanics2nd Semester [5] Flow of An Incompressible Fluid Dr. Sameer Shadeed
5 Bernoulli s Equation 5 Fluid Mechanics2nd Semester [5] Flow of An Incompressible Fluid Dr. Sameer Shadeed
6 Bernoulli s Equation Pressure head Velocity head Elevation head Constant 6 Fluid Mechanics2nd Semester [5] Flow of An Incompressible Fluid Dr. Sameer Shadeed
7 The Energy Line (EL) and the Hydraulic Grade Line (HGL) Each term in the Bernoulli s equation is a type of head P/g = Pressure Head V 2 /2g n = Velocity Head Z = Elevation head EL is the sum of these three heads HGL is the sum of the elevation and the pressure heads 7 Fluid Mechanics2nd Semester [5] Flow of An Incompressible Fluid Dr. Sameer Shadeed
8 The Energy Line (EL) and the Hydraulic Grade Line (HGL) 8 Fluid Mechanics2nd Semester [5] Flow of An Incompressible Fluid Dr. Sameer Shadeed
9 The Energy Line (EL) and the Hydraulic Grade Line (HGL) Understanding the graphical approach of EL and HGL is key to understanding what forces are supplying the energy that water holds 1 P/ g V 2 /2g Z EL HGL Q 2 V 2 /2g P/g Z Point 1: Majority of energy stored in the water is in the Pressure Head Point 2: Majority of energy stored in the water is in the elevation head If the tube was symmetrical, then the velocity would be constant, and the HGL would be level 9 Fluid Mechanics2nd Semester [5] Flow of An Incompressible Fluid Dr. Sameer Shadeed
10 Bernoulli s Equation (Uniform Cross Section) For uniform cross sections streamtubes, the velocity a cross the entire section is uniform as a result Bernoulli s equation becomes: 10 Fluid Mechanics2nd Semester [5] Flow of An Incompressible Fluid Dr. Sameer Shadeed
11 Example 1 11 Fluid Mechanics2nd Semester [5] Flow of An Incompressible Fluid Dr. Sameer Shadeed
12 Example 1 (Solution) 12 Fluid Mechanics2nd Semester [5] Flow of An Incompressible Fluid Dr. Sameer Shadeed
13 Application of Bernoulli s Equation Torricelli s theorem 13 Fluid Mechanics2nd Semester [5] Flow of An Incompressible Fluid Dr. Sameer Shadeed
14 Torricelli s Theorem An ideal fluid is one that is incompressible and has no resistance to shear stress. Ideal fluids do non actually exist, but sometimes it is useful to consider what happen to an ideal fluid in a particular fluid flow problem in order to simplify the problem 14 Fluid Mechanics2nd Semester [5] Flow of An Incompressible Fluid Dr. Sameer Shadeed
15 Torricelli s Theorem Taking the datum at the center of the nozzle and choosing the center streamline give h = z + p/g in the reservoir where velocities are negligible Writing Bernoulli s equation for a streamline between the reservoir and the tip of the nozzle shown as in Fig. 5.4 p1 z 1 h p2 V 2g 2 n, Torricelli's equation resultsif p 2 0 h V 2g 2 n V 2g n h 15 Fluid Mechanics2nd Semester [5] Flow of An Incompressible Fluid Dr. Sameer Shadeed
16 For freely falling body Torricelli s Theorem as u V h g V g V h h g V n n n Fluid Mechanics2nd Semester [5] Flow of An Incompressible Fluid 16 Dr. Sameer Shadeed
17 Torricelli s Theorem (Free Jets) The velocity of a jet of water is clearly related to the depth of water above the hole The greater the depth, the higher the velocity 17 Fluid Mechanics2nd Semester [5] Flow of An Incompressible Fluid Dr. Sameer Shadeed
18 Example 2 18 Fluid Mechanics2nd Semester [5] Flow of An Incompressible Fluid Dr. Sameer Shadeed
19 Example 2 (Solution) 19 Fluid Mechanics2nd Semester [5] Flow of An Incompressible Fluid Dr. Sameer Shadeed
20 Example 2 (Solution) 20 Fluid Mechanics2nd Semester [5] Flow of An Incompressible Fluid Dr. Sameer Shadeed
21 Example 2 (Solution) 21 Fluid Mechanics2nd Semester [5] Flow of An Incompressible Fluid Dr. Sameer Shadeed
22 Example 2 (Solution) 22 Fluid Mechanics2nd Semester [5] Flow of An Incompressible Fluid Dr. Sameer Shadeed
23 Example 3 23 Fluid Mechanics2nd Semester [5] Flow of An Incompressible Fluid Dr. Sameer Shadeed
24 Example 3 (Solution) 24 Fluid Mechanics2nd Semester [5] Flow of An Incompressible Fluid Dr. Sameer Shadeed
25 Example 3 (Solution) 25 Fluid Mechanics2nd Semester [5] Flow of An Incompressible Fluid Dr. Sameer Shadeed
26 Application of Bernoulli s Equation 26 Fluid Mechanics2nd Semester [5] Flow of An Incompressible Fluid Dr. Sameer Shadeed
27 Application of Bernoulli s Equation stagnation point 27 Fluid Mechanics2nd Semester [5] Flow of An Incompressible Fluid Dr. Sameer Shadeed
28 Stagnation Points On any body in a flowing fluid, there is a stagnation point. Some fluid flows over and some under the body. The dividing line (the stagnation streamline) terminates at the stagnation point. The velocity decreases as the fluid approaches the stagnation point. The pressure at the stagnation point is the pressure obtained when a flowing fluid is decelerated to zero speed stagnation point 28 Fluid Mechanics2nd Semester [5] Flow of An Incompressible Fluid Dr. Sameer Shadeed
29 Example 4 29 Fluid Mechanics2nd Semester [5] Flow of An Incompressible Fluid Dr. Sameer Shadeed
30 Example 4 (Solution) 30 Fluid Mechanics2nd Semester [5] Flow of An Incompressible Fluid Dr. Sameer Shadeed
31 Example 5 Determine the difference in pressure between points 1 and 2. Hint: Point 1 is called a stagnation point, because the air particle along that streamline, when it hits the biker s face, has a zero velocity 31 Fluid Mechanics2nd Semester [5] Flow of An Incompressible Fluid Dr. Sameer Shadeed
32 Example 5 (Solution) Assume a coordinate system fixed to the bike (from this system, the bike is stationary, and the world moves past it). Therefore, the air is moving at the speed of the bike. Thus, V 2 = Velocity of the Biker Apply Bernoulli s equation from 1 to 2 Point 1 = Point 2 P 1 /g air + V 12 /2g + z 1 = P 2 /g air + V 22 /2g + z 2 Knowing the z 1 = z 2 and that V 1 = 0, we can simplify the equation P 1 /g air = P 2 /g air + V 22 /2g P 1 P 2 = ( V 22 /2g ) g air 32 Fluid Mechanics2nd Semester [5] Flow of An Incompressible Fluid Dr. Sameer Shadeed
33 Example 5 (Solution) If the Biker is traveling at 5 m/s, what pressure does he feel on his face if the g air = N/m 3? We can assume P 2 = 0, because it is only atmospheric pressure P 1 = ( V 22 /2g )(g air ) P 1 = ((5) 2 /(2(9.81)) x P 1 = 15.3 N/m 2 (gage pressure) If the biker s face has a surface area of 300 cm 2 He feels a force of 15.3 x 300x104 = 0.46 N 33 Fluid Mechanics2nd Semester [5] Flow of An Incompressible Fluid Dr. Sameer Shadeed
34 Application of Bernoulli s Equation 34 Fluid Mechanics2nd Semester [5] Flow of An Incompressible Fluid Dr. Sameer Shadeed
35 Application of Bernoulli s Equation 35 Fluid Mechanics2nd Semester [5] Flow of An Incompressible Fluid Dr. Sameer Shadeed
36 Example 6 36 Fluid Mechanics2nd Semester [5] Flow of An Incompressible Fluid Dr. Sameer Shadeed
37 Example 6 (Solution) 37 Fluid Mechanics2nd Semester [5] Flow of An Incompressible Fluid Dr. Sameer Shadeed
38 Example 6 (Solution) 38 Fluid Mechanics2nd Semester [5] Flow of An Incompressible Fluid Dr. Sameer Shadeed
39 Example 6 (Solution) 39 Fluid Mechanics2nd Semester [5] Flow of An Incompressible Fluid Dr. Sameer Shadeed
40 Application of Bernoulli s Equation 40 Fluid Mechanics2nd Semester [5] Flow of An Incompressible Fluid Dr. Sameer Shadeed
41 Application of Bernoulli s Equation 41 Fluid Mechanics2nd Semester [5] Flow of An Incompressible Fluid Dr. Sameer Shadeed
42 Example 7 42 Fluid Mechanics2nd Semester [5] Flow of An Incompressible Fluid Dr. Sameer Shadeed
43 Example 7 (Solution) 43 Fluid Mechanics2nd Semester [5] Flow of An Incompressible Fluid Dr. Sameer Shadeed
44 Example 7 (Solution) 44 Fluid Mechanics2nd Semester [5] Flow of An Incompressible Fluid Dr. Sameer Shadeed
45 Example 7 (Solution) 45 Fluid Mechanics2nd Semester [5] Flow of An Incompressible Fluid Dr. Sameer Shadeed
46 Example 7 (Solution) 46 Fluid Mechanics2nd Semester [5] Flow of An Incompressible Fluid Dr. Sameer Shadeed
47 Example 8 47 Fluid Mechanics2nd Semester [5] Flow of An Incompressible Fluid Dr. Sameer Shadeed
48 Example 8 (Solution) 48 Fluid Mechanics2nd Semester [5] Flow of An Incompressible Fluid Dr. Sameer Shadeed
49 Example 8 (Solution) 49 Fluid Mechanics2nd Semester [5] Flow of An Incompressible Fluid Dr. Sameer Shadeed
50 The Work Energy Equation 50 Fluid Mechanics2nd Semester [5] Flow of An Incompressible Fluid Dr. Sameer Shadeed
51 The Work Energy Equation 51 Fluid Mechanics2nd Semester [5] Flow of An Incompressible Fluid Dr. Sameer Shadeed
52 The Work Energy Equation 52 Fluid Mechanics2nd Semester [5] Flow of An Incompressible Fluid Dr. Sameer Shadeed
53 Example 9 53 Fluid Mechanics2nd Semester [5] Flow of An Incompressible Fluid Dr. Sameer Shadeed
54 Example 9 (Solution) 54 Fluid Mechanics2nd Semester [5] Flow of An Incompressible Fluid Dr. Sameer Shadeed
55 Example 9 (Solution) 55 Fluid Mechanics2nd Semester [5] Flow of An Incompressible Fluid Dr. Sameer Shadeed
56 Example 10 Calculate the power output of this turbine 56 Fluid Mechanics2nd Semester [5] Flow of An Incompressible Fluid Dr. Sameer Shadeed
57 Example 10 (Solution) 57 Fluid Mechanics2nd Semester [5] Flow of An Incompressible Fluid Dr. Sameer Shadeed
58 Example 10 (Solution) 58 Fluid Mechanics2nd Semester [5] Flow of An Incompressible Fluid Dr. Sameer Shadeed
59 Example 11 Water is pumped from a large lake into an irrigation canal of rectangular cross section 3 m wide, producing the flow situation shown in the figure. Calculate the required pump power assuming ideal flow. 59 Fluid Mechanics2nd Semester [5] Flow of An Incompressible Fluid Dr. Sameer Shadeed
60 Example 11 (Solution) 60 Fluid Mechanics2nd Semester [5] Flow of An Incompressible Fluid Dr. Sameer Shadeed
61 Example 11 (Solution) 61 Fluid Mechanics2nd Semester [5] Flow of An Incompressible Fluid Dr. Sameer Shadeed
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