Differential Equations - Acceleration and velocity models
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Differential Equations - Acceleration and velocity models
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- P1.) A closed cylindrical tank 1.5 m in diameter and 4 m long is completely filled with gasoline (sp.gr. = 0.82) and accelerated horizontally at 3 m/s². Find the total force acting at the rear wall and at the front wall of the tank. Find also the accelerating force on the fluid mass. Answer: 10.66 kN and F = 17.36 kN Subject: Fluid Mechanic Lesson: Relative Equilibrium of Liquids Fundamentals of Fluid FlowQ.2 Four cars, with a mass of 1500 kg each, are loaded on a 6 m wide, 12 m long small car ferry. How deep, in cm will it sink in the water? A 15.2 В 11.5 C 10.2 D 8.31. What is the net force on a ball of mass 20 kg and volume of 0.2 m^3 when it is submerged underwater?
- 6. A 100 cc block of Styrofoam (density 100 kg/m³) is held by a massless string, attaching the bottom of the block to the bottom of the vat, in a vat of water (density 1 gm/cc) as shown in the diagram. В. What is the tension in the string? С. block in it), i.e. everything (vat, water, block) accelerates downwards with acceleration due to gravity, g. Now what is the tension in the string? Justify your answer. [Hint: Think carefully about how the buoyant force is derived] Now imagine you drop the whole vat of water (with the StyrofoamBalloons are used for touristic travel in certain regions.For this travel, aforce is required to push the balloon upward.The force is expressed as below; ?balloon=pair x g x vballoon.Assume that the balloon has a 500-cm-diameter, the density of air is 1,23x10−3g/cm3. A-definedgas is used to fill the balloons and itsweight is approximately 1:7 of the weight of air.Neglect the other weights. The balloon carries three people. The people’s weights are67, 75 and 83 kg, respectively.Determine the balloon’s acceleration when it is first released.An S-shaped gate (1 m wide) consists of two quarter circles, each of radius 2 meters and rotate (hinged) about the common edge of the two quarter circles. Specific weight of water = 9810 N/m³. 8 m 2m hinge to Water 2 m Open air The total vertical hydrostatic pressure force acting on the gate, in kN is: a.392.4 b.313.9 c.616.4 d.784.8 The total horizontal hydrostatic pressure force acting on the gate, in kN is: A.392.4 B.313.9 C.616.4 D.784.8 A slab of wood 1 m by 1m by 0.25 m (S=0.5) floats in water (specific weight = 9810 N/m³) with a 500 N load on top of it. The submerged volume of the slab in m³ is: a.0.166 b.0.176 c.0.250 d.0.125
- a : 3 area = A A 5 gallon, cylindrical open container with a bottom area of 120 in? is filled with glycerin (SG=1.26) and rests on the floor of an elevator. Notes: The density of water is 62.4 Ibm / ft3. Useful conversion: 1 gal = 231 in3. The weight of the container is negligible. (a) What resultant force does the container exert of the floor of the elevator when the elevator is stopped. F = Ibf (b) Determine the fluid pressure at the bottom of the container when the elevator has an upward acceleration of 3.0 ft/s2. Pb = |Ibf/ f2 (c) What is the resultant force when the elevator accelerates upwards at 3.0 ft'/s?. F = | Ibf3. What is the volume change in cm of a hydraulic oil when subjected to a pressure of magnitude 6 MPa? The original volume of the oil is 1500 cm3 and its bulk modulus of elasticity is 2.1x10 PA. Select one: a. DVol=-7.14 cm3. b. DVol=-8.57 cm3. c. DVol=-4.29 cm3. O d. DVol=-2.49 cm3. e. DVol=-5.71 cm3.An ion-engine-propelled spacecraft has mass 1000 kg without propellant. Its propellant tank is filled with 30 kg of compressed xenon. If the ion engine is operated on orbit at specific impulse 3000 s, what total AVv (in m/s) is available for the mission? (Use 9.81 m/s? as Earth's sea-level gravity.) (m/s)
- 8. The density of air is about 1.24kg/m³ at sea level and virtually zero at upper levels of the atmosphere, so the average density is taken as 0.62kg/m³. If air pressure is assumed to be 1.0x10° Pa and g to be 10 m/s². Estimate the height of the earth's atmosphere.Calculate the pressure at depth 2 m using P = ρgh. p= (pressure) 19.855 kPa p= (density of the liquid) 1000 kg/m3 g= (gravity) 9.8 m/s2 h (height below the free surface of the liquid) 2m6. DETAILS A tennis ball has a volume of 141.00 cm³ and an average density of 275.00 What is the tennis ball's mass, in grams? g kg m³ O 73.37 N MY NOTES What amount of force would need to be applied to cause the tennis ball to be completely submerged in ethyl alcohol (Pethyl alcohol=806- the vertical direction (weight, buoyant force, and applied force). When writing the buoyant force, note that the ball will be fully submerged. What does this do to V?) 1.11 N 0.73 N 0.38 N 38.00 N 7337.36 N ASK YOUR TEACHER kg -)? (HINT: Set up a FBD and look at all the forces acting in