In rotating a thin circular disc submerged in a fluid, a torque has to be applied to the disc to overcome the frictional resistance of the fluid. Using dimensional analysis, show that where T is the applied torque and D is the diameter of a disc rotating at a speed N in fluid of viscosity u and density p.

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

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.

Can you give me the importance of this non slip condition concept to the application of fluid mechanics?

Consider steady viscous flow through a small horizontal tube. For this type of flow, the pressure gradient along the tube, Δp ⁄ ΔL should be a function of the viscosity Y, the mean velocity V, and the diameter D. By dimensional analysis, derive a func- tional relationship relating these variables. Fluid mechanics

This problem involves a cylinder falling Inside a pipe that is filled with oil, is depleted in the figure. The small space between the cylinder and the pipe is labricated with an oll film that has aboolute viscosity j. (a) Derive a formula for the steady rate of descent of a cylinder with weight W, diameter d. and length sliding inside a vertical smooth pipe that has inside diameter D. Aesume that the cylinder is concentric with the pipe as it falls. (b) Use the general formula you derive to find the rate of descent of a cylinder 100mm in diameter that slide inside a 100.5mm diameter pipe. The cylinder is 200mm long and weighs 15N. The lubricant is SAE 2OW oll with a viscosity of 2.0 x 10- Pax.

Determine the rotational speed (in rpm) at which the liquid will start spilling from the edges of the container determine the liquid height at the speed computed in the previous question

Books on porous media and atomization claim that the viscosityμ and surface tension Y of a fl uid can be combinedwith a characteristic velocity U to form an important dimensionlessparameter. ( a ) Verify that this is so. ( b ) Evaluatethis parameter for water at 20°C and a velocity of3.5 cm/s. Note: You get extra credit if you know the nameof this parameter.