CVE 240-03 FLUID MECHANICS

EXAMPLES (HYDROSTATICS)

EXAMPLE 1:

EXAMPLE 2:

PA+1h1-2h2=0 PA+1h1-2h2-3h3=PB

EXAMPLE 3: Determine the gage pressure at point A.

EXAMPLE 4: Determine the gage pressure at point A.

Example 5: What is the gage pressure at point A.

h =4/5 × 50 = 40 cm = 0.4 mPA + γ1 × 0.5 –γ2 × (0.4 – 0.1) = 0PA +10 × 0.5 - 25 × 0.3 = 0PA = 2.5 kPa

Example 6: For Figure below Liquid in the inclined pipe is water and that in the manometer is mercury. If the water is flowing downward, determine the total pressure drop between points 1 and 2.

P1 + 62.4 (15 sin30o + 6/12) – 13.6 × 62.4 × 6/12 = P2

P1 + P2 = 74.88 lb/ft2 = 0.52 psi

Example 7: Determine the density of unknown oil, if atmospheric pressure is 101 kPa and pressure at the base of the tank is 169 kPa. H=0.5m.

101000 + (680 × 4 + 998 × 2 + 0.5 xρoil +1260* 0.2 + 13550 × 0.1) (9.8) =169,000

ρoil x 0.2 × 9.8 = 2330.2. Hence, ρoil = 1189 kg/m3.

Example 8: Determine pressure at point A and B. (water at 20 oC)

PA – 9790 × (1.1 – 0.5 – 0.15) = 0PA = 4405.5 Pa = 4.4 kPa

PB – 9790 × (1.1 – 0.5) = 0PB = 5874 Pa = 5.87 kPa

EXAMPLE 9: A flood gate weighing 2000lb is lying at an inclination of 5o. The center of gravity of the gate is 45 in along the gate from the hinge point. Determine the depth of the water level at the gate will start opening.

Closing moment of the gate = 2000 × (45/12) × sin 5o = 653.67 lb-ft.F = γhcgA = 62.4 × h/2 × [5 x h/cos 5o] = 156.6 h2

Summation of moments about hinge = 0156.6 h2 × [(5 + 10/12) – (h/cos 5o)/3] – 653.67 = 0913.5 h2 – 52.4 h3 – 653.67 = 0h = 0.868 ft.

Example 10: The rectangular gate CD is 2 m wide and 2.5 m long. Neglecting the friction at the hinge C, determine the weight of the gate necessary to keep it shut until the water level rises to 2m above the hinge.

Example 11: A 2-m wide gate OAB is hinged at O and rest against a rigid support at B as shown in Figure 4. What minimum horizontal force, P, is required to hold the gate closed? Neglect the weight of the gate

Example 4.12: The concrete dam weighs 23.6 kN/m3 and rests on a solid foundation. Determine the minimum coefficient of friction between the dam and the foundation required to keep the dam from sliding. Base your analysis on a unit length of the dam.

SOLUTION:= tan-1 = 5/4 = 51.3º

EXAMPLE 4.18: The 2-m-diameter gate, Figure 4.18, swings around a horizontal pivot C located 50 mm below the center of the gate. To what depth, h, can the water rise without causing anunbalanced clockwise moment about pivot C?

EXAMPLE 4.14: Suppose a vertical flat plate supports water on one side and oil of specific gravity 0.86 on the other side, as shown in Figure below. How deep should the oil be so that there is no net

horizontal force on the plate? Calculate the moments of the pressure forces about the base of the plate. Are the magnitudes of the moment equal? Why? THIS IS FOR YOU TO SOLVE.

Examles 1-13 were taken Elementary Hydraulics by Cruise et al., and 14 was taken Water Resources Eng. By Mays.