A boy threw a rubber ball into a lake. The spherical rubber ball has a diameter of 7.5 cm and a density of 1100 kg/m³ was dropped into the lake water with a temperature of 25°C. i. Determine the terminal velocity of the ball in the water. ii. Prove that the assumption you made for answering (i) is correct
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Subject : Thermofluid
Question : A boy threw a rubber ball into a lake. The spherical rubber ball has a diameter of 7.5 cm and a density of 1100 kg/m³ was dropped into the lake water with a temperature of 25°C.
i. Determine the terminal velocity of the ball in the water.
ii. Prove that the assumption you made for answering (i) is correct
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- In an oil pool, a small steel ball is released from the surface (y=0) without initial velocity. The strength of the resistance force exerted by the oil against the movement of the ball is directly proportional to the speed of the ball (Fd = k*V , k: constant). Neglect the buoyant force exerted by the oil. (m = 0.2kg, k = 0.843550 kg/s, g = 9.81 m/s^2). a-) What is the limit speed of ball ( Vlim)? b-) What is the time it takes for the speed of the ball to reach 99% of the limit speed after it is released from the surface? c-) What is the depth at which the ball's velocity reaches 99% of the limit velocity after it is released from the surface?Control volume concept can be used to obtain forces in both internal and external flow. By drawing a control volume around a region of fluid to expose the stresses acting on the boundaries and applying the conservation of mass and conservation of momentum in integral form, the net forces acting on the fluid and hence the reaction forces acting on the solid boundary can be calculated. The advantages of this approach over differential approach are: (i) It is an easy way to obtain net forces. (ii) It gives a detailed understanding of how these forces are generated. (iii) It is commonly used in engineering practice to obtain reaction forces on pump, turbine, elbow, etc. for the design of anchoring fixtures/foundation. (A) (B) (C) (D) (i) and (ii) (i) and (iii) (ii) and (iii) All of the above200 pm 0.12 cm Fluid Stationary cylinder 4 In regions far from the entrance, fluid flow through a circular pipe is one-dimensional, and the velocity profile for laminar flow is given by u(r) = Umax(1 - r/R9), where R is radius of the pipe, r is the radial distance from the center of the pipe, and Umax is the maximum flow velocity, which occurs at the center. Obtain (a) a relation for the drag force applied by the fluid on a section of the pipe length L and (b) the value of the drag force for water flow at 20°C with R = 0.08 m, L = 15 m, Umax = 3 m/s, and u = 0.0010 kg/m.s. %3D
- (a) Determine a differential equation for the velocity v(t) of a mass m sinking in water that imparts a resistance proportional to the square of the instantaneous velocity (with a constant of proportionality k > 0) and also exerts an upward buoyant force whose magnitude is given by Archimedes' principle, which states that the upward buoyant force has magnitude equal to the weight of the water displaced. Assume that the positive direction is downward. (Let V be the volume of the object, p the weight density of water, and g the acceleration due to gravity.) dv pVg dt m m (b) Solve the differential equation in part (a). ** (v- ) () mg k mg V - v(t) k (c) Determine the limiting, or terminal, velocity of the sinking mass. mg k lim v(t) =Construct a flow diagram illustrating the mass and energy exchange between a shining light bub and its surroundings. Include also if energy is generated or consumed within the system boundary. Is it movable or rigid?A centrifuge with a diameter of 1.2 m and a height of 40 cm must spin at what rpm. For a suspension with particles bigger than 25 microns, a liquid thickness of 18-cm in the bowl that flows out at a rate of 100 L/min? Particles have a density of 1250 kilograms per cubic meter. The density of the water is 991 kg/m^3, with a viscosity of 0.88 cP.
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