Q: inside
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Q: The differential change in pressure p close to the surface of a static fluid is given by the…
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Q: 15 A 120-kg ancient statue lies at the bottom of the sea. Its volume is (6 x 10^6) mm^3. How much…
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Q: continuity equation
A: Equation of continuity A₁v₁ = A₂v₂
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- The continuity equation for the flow of a fluid can be obtained as a logical consequence of the fundamental physical principle called: Answers: a) conservation of momentum. b) conservation of charge. c) conservation of mass. d) energy conservation.The differential change in pressure p close to the surface of a static fluid is given by the following expression: dp/dy = -3Ap2,where A is a constant, with units of 1/(atm•m), and p is the pressure in atm. The pressure at the surface of the fluid is p(0) = 1 atm, and the coordinate y here is positive upwards with origin at the surface. Write an expression for the absolute pressure as a function of y.An airplane has wings, each with area 3.85 m2, designed so that air flows over the top of the wing at 248 m/s and underneath the wing at 226 m/s. Approximately what size wings would an aircraft need on Mars if its engine generates the same differences in speed as in the "Practice It" and the total mass of the craft is 300 kg? The density of air on the surface of Mars is approximately one percent Earth's density at sea level, and the acceleration of gravity on the surface of Mars is about 3.8 m/s2. ______________m2
- Prove that, the dimensional analysis of the physical quantities forces, pressure and energy are MLT-2 , ML-1T-2 and ML2T-2 respectivelyThe velocity field of a fluid v (in meters per second) has divergence div(v)(P) = 3 at the point P = (2, 2, 2). Estimate the flow rate out of the sphere of radius 0.5 meter centered at P.Relative equilibrium is the condition where every particle of a liquid is at rest with respect to every particle and to the containing vessel, but the whole mass, excluding the vessel, has a uniform accelerated motion with respect to the earth. TRUE FALSE
- A toy duck is floating on the water. The average density of the duck is ρd = 760 kg/m3, while the density of water is ρ = 1.0 x 103 kg/m3. The volume of the duck is Vd = 0.00011 m3.Randomized Variables ρd = 760 kg/m3Vd = 0.00011 m3 a)Express the magnitude of the buoyant force, F, in terms of ρ and the volume of water that the duck displaces, Vw. b)Express the volume of the duck in water, Vw, in terms of ρ, ρd and Vd. c) Calculate the numerical value of the volume of the duck in water, Vw in m3.A cube of side length ℓℓ and density ρcρc is immersed in a fluid of density ρflρfl. Let hh be the height of the cube that is immersed in the fluid. Then, a slight downward push is applied on the cube, making it oscillate up and down the fluid. Determine the period for small oscillations of the cube. Express your final answer in terms of h.A toy duck is floating on the water. The average density of the duck is ρd = 760 kg/m3, while the density of water is ρ = 1.0 x 103 kg/m3. The volume of the duck is Vd = 0.00011 m3.Randomized Variables ρd = 760 kg/m3Vd = 0.00011 m3 a) Express the weight of the duck, W, in terms of ρd and Vd. b)Calculate the numerical value of W in Newtons. c) Express the magnitude of the buoyant force, F, in terms of ρ and the volume of water that the duck displaces, Vw.
- A spherical particle falling at a terminal speed in a liquid must have the gravitational force balanced by the drag force and the buoyant force. The buoyant force is equal to the weight of the displaced fluid, while the drag force is assumed to be given by Stokes Law:Fd = 6πRηv,where R is the radius of the object, η is the coefficient of viscosity in the fluid, and v is the terminal speed. a) Give the equation for terminal speed in the variables from Stokes law, and the densities of the sphere ρs and the fluid ρ1. b) Using the equation of the previous step, find the viscosity of motor oil (in kg/m/s) in which a steel ball of radius 0.95 mm falls with a terminal speed of 4.34 cm/s. The densities of the ball and the oil are 7.7 and 0.72 g/mL, respectively.The gas tank of a car is filled with a nozzle that discharges gasoline at a constant flow rate. Based on unit considerations of quantities, obtain a relation for the filling time in terms of the volume V of the tank (in L) and the discharge rate of gasoline V (in L/s).Find the weight of the air in a living room with a 4.0 m x 5.0 m floor and a ceiling 3.0 m high. (Give your answer in N.) The density of air is 1.29x10 kg/m3.