prove that the pressure at a point in a fluid at rest, or in motion, is independent of direction as long as there are no shearing stresses present and what this important result known ?

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.

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

(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