Starting from the principle of conservation of mass, obtain the expression of the continuity equation for fluids: a) compressible, b) incompressible; obtain the equation for the flow of a given system.
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Starting from the principle of conservation of mass, obtain the expression of the continuity equation for fluids: a) compressible, b) incompressible; obtain the equation for the flow of a given system.
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- Water is flowing in the pipe shown in the figure below, with the 8.10-cm diameter at point 1 tapering to 3.05 cm at point 2, located y = 11.0 cm below point 1. The water pressure at point 1 is 3.20 x 104 Pa and decreases by 50% at point 2. Assume steady, ideal flow. What is the speed of the water at the following points? (a) point 1 (b) point 2 m/s m/sAST Water is flowing in the pipe shown in the figure below, with the 8.20-cm diameter at point 1 tapering to 3.85 cm at point 2, located y 12.5 cm below point 1. The water pressure at point 1 is 3.20 x 10 Pa and decreases by 50% at point 2. Assume steady, ideal flow. What is the speed of the water at the following points? (a) point 1 x Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. m/s (b) point 2 x Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. m/sVerify that work input equals work output for a hydraulic system assuming no losses due to friction. Do this by showing that the distance the output force moves is reduced by the same factor that the output force is increased. Assume the volume of the fluid is constant. What effect would friction within the fluid and between components in the system have on the output force? How would this depend on whether or not the fluid is moving?
- As a fuel saving measure, commercial jets cruise at an altitude of about 10 km. While cruising at an altitude of 10 km, a small leak occurs in one of the window seals in the passenger compartment of an Airbus. Within the passenger compartment, the pressure and temperature are, respectively, 1.01 atm and 20°C and the pressure outside the craft is 0.311 atm. Model the air as an ideal fluid to find the speed (in m/s) of the stream of air flowing through the leak. (Assume the density of air to be 1.20 kg/m³.) m/sThree solid objects are floating in a liquid, as in the drawing. They have different weights and volumes, but have the same thickness (the dimension perpendicular to the screen). Rank the objects according to their density, largest first. O A, C, B O A, B, C O B, A, C O B, C, A O C, A, B CQuestion 1 a) Consider the forces acting on an infinitesimal fluid element located at radius r inside a star, where the star is in hydrostatic equilibrium. Show that the buoyancy force acting on the fluid element may be written as Pe dv dt = -(Pe - p)g where Pe is the density inside the fluid element, p is the density of the gas in the surrounding gas at radius r, v is the velocity of the fluid element and g is local acceleration due to gravity. For full marks you should explain each step of your derivation. b) With the aid of a diagram, explain the condition required for convection to occur by considering the small displacement of a fluid element from its original equilibrium location within a star.