Static Surface Forces. Forces on Curved Surfaces: Horizontal Component. Forces on Curved Surfaces. Hydrostatic Forces on Curved Surfaces

Size: px

Start display at page:

Download "Static Surface Forces. Forces on Curved Surfaces: Horizontal Component. Forces on Curved Surfaces. Hydrostatic Forces on Curved Surfaces"

Suzan Hubbard
5 years ago
Views:

the horizontal omponent of pressure fore on a urved surfae equal to?

1 Hdrostati Fores on Curved Surfaes Stati Surfae Fores Fores on plane areas Fores on urved surfaes Buoant fore Stabilit of floating and submerged bodies Fores on Curved Surfaes Horizontal omponent Vertial omponent Fores on Curved Surfaes: Horizontal Component What is the horizontal omponent of pressure fore on a urved surfae equal to? The pressure fore on the vertial plane projetion The enter of pressure is loated using the moment of inertia or pressure prism tehnique. The horizontal omponent of pressure fore on a losed bod is. zero

h r F F 0 F FCB W F W FCB What if the up had sloping sides?

2 Fores on Curved Surfaes: Vertial Component What is the magnitude of the vertial omponent of fore on the up? Pressure on Curved Surfae p F x F 0 x FC Fx FC Fx F = p p = h F = hr 2 =W! h r F F 0 F FCB W F W FCB What if the up had sloping sides? Fores on Curved Surfaes: Vertial Component The vertial omponent of pressure fore on a urved surfae is equal to the weight of liquid vertiall above the urved surfae and extending up to the (virtual or real) free surfae. F pi C W F VBCD W

3 Example: Fores on Curved Surfaes Find the resultant fore (magnitude and loation) on a 1 m wide setion of the irular ar. F V = W 1 + W 2 3 m W 1 = (3 m)()(1 m) +1/4() 2 (1 m) = 58.9 kn kn = 89.7 kn W 2 F H = p p h = (4 m)()(1 m) = 78.5 kn x Example: Fores on Curved Surfaes The vertial omponent line of ation goes through the entroid of the volume of above the surfae. Take moments about a vertial axis through. 4 4() xfv ( 1m) W1 W2 3 3 p x 4() (1 m)(58.9 kn) (30.8 kn) 3 (89.7 kn) 3 m = m (measured from ) with magnitude of 89.7 kn W 1 W 2 Example: Fores on Curved Surfaes The loation of the line of ation of the horizontal omponent is given b I x = + b ba I x = 12 I = x 3 = 4 m = m + 4 m = m (1 m)() 3 /12 = m 4 ( 4 m )( [ )( 1 m ) ] ( ) a 3 m W 1 W 2 x Example: Fores on Curved Surfaes m m 78.5 kn 89.7 kn kn horizontal vertial resultant

1.083 m 78.5kN Clindrial Surfae Fore Chek C 0.948 m 89.7kN ll pressure fores pass through point C. The pressure fore applies no moment about point C. The resultant must pass through point C. (78.

948m) = 0 Stati Surfae Fores Summar Fores aused b gravit (or ) total aeleration on submerged surfaes horizontal surfaes (normal to total aeleration) F = g h Loation where p = p ref inlined surfaes (

4 1.083 m 78.5kN Clindrial Surfae Fore Chek C m 89.7kN ll pressure fores pass through point C. The pressure fore applies no moment about point C. The resultant must pass through point C. (78.5kN)(1.083m) - (89.7kN)(0.948m) = 0 Stati Surfae Fores Summar Fores aused b gravit (or ) total aeleration on submerged surfaes horizontal surfaes (normal to total aeleration) F = g h Loation where p = p ref inlined surfaes ( oordinate has origin at free surfae) F I h x urved surfaes Horizontal omponent F h Vertial omponent ( ) weight of fluid above surfae Buoant Fore The resultant fore exerted on a bod b a stati fluid in whih it is full or partiall submerged The projetion of the bod on a vertial plane is alwas. zero The vertial omponents of pressure on the top and bottom surfaes are different rhimedes Priniple rhimedes Priniple F B = weight displaed fluid Line of ation passes through the entroid of displaed volume

Buoant Fore: Line of tion The buoant fore ats through the entroid of the displaed volume of fluid (enter of buoan) = volume d = distributed fore x = entroid of volume Sea (=10.

The buo normall floats on the surfae, at other times the depth inreases so that the buo is ompletel immersed as shown. What is the tension in the able? F 0 FB W T 3 3 3 F B d (10,100 N / m ) (1.

5 Buoant Fore: Line of tion The buoant fore ats through the entroid of the displaed volume of fluid (enter of buoan) = volume d = distributed fore x = entroid of volume Sea (=10.1 kn/m 3 ) Buo F B W T Cable Example Spherial buo has a diameter of 1.5 m, weighs 8.50 kn, and is anhored to the sea floor with a able as shown. The buo normall floats on the surfae, at other times the depth inreases so that the buo is ompletel immersed as shown. What is the tension in the able? F 0 FB W T F B d (10,100 N / m ) (1.5 m) 17, 850 N 6 6 T FB W 17,850 8,500 N 9,350 N Buoant Fore: ppliations Using buoan it is possible to determine: Weight of an objet Volume of an objet Speifi gravit of an objet F 1 1 > 2 1 W F 2 Fore balane 2 W (With F 1, F 2, 1, and 2 given) Hdrometer Buoant fore F B = weight of the hdrometer must remain onstant Hdrometer floats deeper or shallower depending on the speifi weight of the fluid

h 1 2 S = 0.821 S = 0.780 Example hdrometer weighs 0.0216 N and has a stem at the upper end that is lindrial and 2.8 mm in diameter.

821*9810* V1 6 3 V1 2.68x10 m Whdrometer Wdisplaed 0.0216 0.780*9810*( V1 h) 6 2 0.780*9810*[2.68x10 (0.0028) h] 4 h 0.0232m 23.

The aptain is in a hurr to get to shore and deides to ut the anhor off and toss it overboard to lighten the boat.

6 h 1 2 S = S = Example hdrometer weighs N and has a stem at the upper end that is lindrial and 2.8 mm in diameter. How muh deeper will it float in oil of S=0.78 than in alohol of S=0.821? For position 1: Whdrometer Wdisplaed For position 2: *9810* V1 6 3 V1 2.68x10 m Whdrometer Wdisplaed *9810*( V1 h) *9810*[2.68x10 (0.0028) h] 4 h m 23.m sailboat is sailing on Caspian sea. The aptain is in a hurr to get to shore and deides to ut the anhor off and toss it overboard to lighten the boat. Does the level of Caspian sea inrease or derease? Wh? The anhor displaes less when it is ling on the bottom of the lake than it did when in the boat. otational Stabilit of Submerged Bodies Exerise: 2.89, 2.84, 2.95, ompletel submerged bod is stable when its enter of gravit is below the enter of buoan B G B G

Forces on curved surfaces Buoyant force Stability of floating and submerged bodies

Forces on curved surfaces Buoyant force Stability of floating and submerged bodies Stti Surfe ores Stti Surfe ores 8m wter hinge? 4 m ores on plne res ores on urved surfes Buont fore Stbilit of floting nd submerged bodies ores on Plne res Two tpes of problems Horizontl surfes (pressure