An-Najah National University Civil Engineering Departemnt. Fluid Mechanics. Chapter [2] Fluid Statics

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1 An-Najah National University Civil Engineering Deartemnt Fluid Mechanics Chater [2] Fluid Statics 1

2 Fluid Statics Problems Fluid statics refers to the study of fluids at rest or moving in such a manner that no shearing stresses exist in the fluid These are relatively simle roblems since no velocity gradients exist. Thus, viscosity does not lay a role Alications include the hydraulic ressure, manometry, dams, and fluid containment (tanks) 2

3 Pressure (P) is the force er unit area, where the force is erendicular to the area F (N) P (N/m 2 or Pa) = A (m2 ) Pressure 1 kn/m 2 = 1 kpa 1 kpa = si Pressure in a fluid acts equally in all directions Pressure in a static liquid increases linearly with deth ressure increase = γ h increase in deth (m) 3

4 Pressure at a Point Pressure is a scalar quantity that is defined at every oint within a fluid Force balance in the x-direction: 4

5 Pressure at a Point Force balance in the z-direction: Vertical force on A Vertical force on lower boundary Total weight of wedge element 5 = secific weight

6 From last slide: Pressure at a Point Divide through by to get Now shrink the element to a oint: This can be done for any orientation, so 6

7 Pressure at a Point The result shows that ressure at any oint in a fluid at rest has a single value, indeendent of direction as long as there are no shearing stresses (or velocity gradients) resent in the fluid For fluids in motion with shearing stresses, this result is not exactly true, but is still a very good aroximation for most flows 7

8 Pressure Transmission In a closed system, ressure changes from one oint are transmitted throughout the entire system (Pascal s Law). F out A A out in F in Hydraulic Lift 8

9 Pressure Variation with Elevation Static fluid: All forces must balance as there are no accelerations Look at force balance in direction of l 9

10 Pressure Variation with Elevation From the revious figure, note that Shrink cylinder to zero length: From the revious slide: or 10

11 Pressure Variation with Elevation The ressure-elevation relation derived on the revious slide, is erfectly general (alies also to variable g) But if g is constant, the above equation is easy to integrate: The quantity and is known as the iezometric ressure is called the iezometric head 11

12 Pressure Variation with Elevation For an incomressible fluid (g is constant), ressure and elevation at one oint can thus be related to ressure and elevation at another oint as: g z 1 2 z 1 z2 or 2 or z 1 h 1 g g z z ) gh 1 g 2 Constant 2 (

13 13 Absolute and Gage Pressure

14 14 Absolute and Gage Pressure

15 Examle 1 Solution: 15

16 Examle 2 What is the water ressure at a deth of 35 ft? Solution: With the information given, all we can calculate is the ressure difference between oints 1 and 2 16

17 Examle 3 What is the gage ressure at oint 3? Solution: Two ste solution: 1) Calculate 2) Calculate s.g.= (relative to atmosheric ressure at oint 1)

18 Pressure Measurement Mechanical Pressure Gages The Bourdon ressure and Aneroid barometer are tyical mechanical devices for measuring gage and absolute ressures, resectively 18

19 Pressure Measurement Liquid Pressure Gages Manometer: gravimetric device based uon liquid level deflection in a tube Mercury barometer: evacuated glass tube with oen end submerged in mercury 19

20 The Manometer Simle, accurate device for measuring small to moderate ressure differences Rules of Manometry: ressure change across a fluid column of height h is gh ressure increases in the direction of gravity, decreases in the direction oosing gravity two oints at the same elevation in a continuous static fluid have the same ressure 20

21 The Manometer 1 gl 2 0 g h x 1 21

22 The Manometer g l 4 x 1 1 y g l g h 22

23 The Manometer 1 atm 0( gage) g g m m 3 h h lg 2 lg

24 Examle 4 Find the location of the surface in the manometer Solution: The distance h is the height of the liquid in the manometer above the heavier liquid in the tank A B D C C hg m B h 10g 10g g m w w cm 24

25 Examle 5 Find the gage ressure at the ie center A C Solution: Manometer equation from the ie center to the oen end of the manometer A A 0( gage) C 2.5(1)(62.4) 0 1(2)(62.4) 0.5(1)(62.4) C 25

26 26 Examle 6

27 27 Examle 6 (Solution)

28 Find the secific weight of the fluid which filled art CD of the tube Solution: D V 2 d h 4 (0.5) 4 2 h 2cm Manometer Equation A ( h 0.05)g hg Examle 7 3 liq h cm D A B h C 2 cm 3 g liq ( h 0.05) g h ( ) (9810) g liq A 4995 N D / m 3 o(gage) 28

29 Differential Manometer Used for measuring ressure differences between oints along a ie g w l 1 g wl g mh g w l h) ( 2 g m ( ) h g g 2 1 w m 29

30 Find the change in iezometric ressure and in iezometric head between oints 1 and 2. Solution: Manometer equation from oint 2 to oint 1 In general Examle 8 (iezometric ressure) (iezometric head) 30

31 31 Examle 9

32 32 Examle 9 (Solution)

33 33 Examle 9 (Solution)

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