A vertical U-tube partially filled with alcohol (SG= 0.99) is rotated at a specified rate about its left arm. Compute for the following: (a) angular velocity of the tube's rotation if the alcohol is on the brink of spilling (b) pressure at point B during the rotation of the tube Please provide explanation per line of solution. thanks 10 cm 20 cm B +12.5 cm - 12.5 cm 25 cm

An infinite plate is moved over a second plate on a layer of liquid as shown. For small gap width, d, we assume a linear velocity distribution in the liquid. The liquid kinematic viscosity is 0.00739 cm²/s and its density is 880 kg/m³. Determine the shear stress on the upper plate, in N/m?. y U = 0.3 m/s d = 0.3 mm

1.What is the difference between laminar and turbulent flow, and how does this affect fluid mechanics in mechanical engineering?

A solid sphere having diameter 5 mm is falling through oil of density 800 kg/m? and dynamic viscosity 0.8 kg/m-s at a constant velocity of 1 cm/s. Drag force on the sphere

(b) In two dimensional boundary layer, shear stress was changed linearly from the solid surface toward y-axis until it reach the value of zero at y = ở. Based on Table 2 and setting given to you; (i) Derive the equation of displacement thickness and momentum thickness using Von Karman Approximation Method ; and (ii) Determine the accuracy of this method in determining the value of displacement thickness and momentum thickness. C5 Table 2: Equation of Velocity Profile Setting Equation wU = 2y/8 - (y/S² 1

A cube of lead with a side dimension of 5.0 cm is slowly lowered into the beaker of oil by a thin string attached to a spring scale at a constant rate, as shown in the figure. The density of lead is 11,300 kg/m³. oil density: 960 kg/m3 1 2 3 0.0010 m³ beaker i. What will be the spring scale reading in newtons when the lead has been submerged to location 2? ii. Does the spring scale reading increase, decrease, or stay the same when the cube is lowered from location 2 to location 3? Justify your answer by referencing the pressure of the fluid on the lead cube. iii. The lead cube is lowered from above the oil's surface (location 1) to a spot just below the surface (location 2) until the cube is just above the bottom of the beaker (location 3). Describe any changes in pressure on the bottom of the beaker during this process. Explain your answer.

(b) In two dimensional boundary layer, shear stress was changed linearly from the solid surface toward y-axis until it reach the value of zero at y = 6. Based on Table 2 and setting given to you; () Derive the equation of displacement thickness and momentum thickness using Von Karman Approximation Method ; and (ii) Determine the accuracy of this method in determining the value of displacement thickness and momentum thickness. Table 2 : Equation of Velocity Profile Setting Equation wU = 3(y/8)/2 – (y/8j?/2

Consider a Falling Sphere Viscometer, which is used to measure the viscosity μ of a fluid by observing the terminal velocity of a heavy sphere (density Ps and diameter D) falling under gravity in a column of the fluid (density pf). (a) Use Dimensional Analysis to derive a formula for the drag force exerted on the sphere by the viscous fluid when it is moving at speed v through the fluid. (b) How is the terminal velocity of the sphere related to the fluid viscosity? (c) If the sphere starts from rest, use Dimensional Analysis to predict the timescale over which the sphere will reach its terminal velocity. Please use dimensiona analysis to solve the problem Answr for part a= Fd=KmuVD answer for part b=V=Fd/kmuD Please solve only for part C (part a and b no need to solve)and expalin in detail Thanks

We want to predict the drag force on a remote-control airplane as it flies through air having a density of 1.21 kg/m³ and a viscosity of 1.76x10- Pa-s. The airplane's fuselage has a diameter of 200 mm and the airplane will fly through air at a speed of 32 m/s. A model of the airplane's fuselage will be tested in a pressurized wind tunnel. The diameter of the model is 75 mm and the density and viscosity of the air in the wind tunnel are 3.00 kg/m³ and 1.82× 10-5 Pa-s, respectively. a) The diameter of the airplane's fuselage will be used to define the Reynolds number Re, for the flow around the fuselage. Compute the Reynolds number for the flow around the airplane's fuselage (answer: Re, = 4.40x 10'). b) Find the speed of the air that should be used to test a model of the fuselage in the wind tunnel to correctly model dynamic conditions (answer: 35.6 m/s). c) The model is tested in the wind tunnel at four speeds that bracket the speed computed above. The measured drag forces on the…