A rotating viscometer consists of two concentric cylinders-a stationary inner cylinder of radius R, and an outer cylinder of inside radius Ro rotating at angular velocity (rotation rate) wo. In the tiny gap between the two cylinders is the fluid whose viscosity (u) is to be measured. The length of the cylinders (into the page in Figure 1) is L. L is large such that end effects are negligible (we can treat this as a two-dimensional problem). Torque (T) is required to rotate the outer cylinder at constant speed. Showing all your work and algebra, generate an approximate expression of T as a function of the other variables. Liquid: p, H. R₂ Stationary inner cylinder Rotating outer cylinder

A rotating viscometer consists of two concentric cylinders-a stationary inner cylinder of radius R, and an outer cylinder of inside radius Ro rotating at angular velocity (rotation rate) wo. In the tiny gap between the two cylinders is the fluid whose viscosity (u) is to be measured. The length of the cylinders (into the page in Figure 1) is L. L is large such that end effects are negligible (we can treat this as a two-dimensional problem). Torque (T) is required to rotate the outer cylinder at constant speed. Showing all your work and algebra, generate an approximate expression of T as a function of the other variables. Liquid: p, H. R₂ Stationary inner cylinder Rotating outer cylinder

Refrigeration and Air Conditioning Technology (MindTap Course List)

8th Edition

ISBN:9781305578296

Author:John Tomczyk, Eugene Silberstein, Bill Whitman, Bill Johnson

Publisher:John Tomczyk, Eugene Silberstein, Bill Whitman, Bill Johnson

Chapter11: Calibrating Instruments

Section: Chapter Questions

Problem 4RQ: Temperature-measuring instruments may be designed to measure the temperature of vapors, ________,...

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A rotating viscometer consists of two concentric cylinders—a stationary inner cyliner of radius Ri and an outer cylinder of inside radius Ro rotating at angular velocity (rotation rate) ?o. In the tiny gap between the two cylinders is the fluid whose viscosity (? ) is to be measured. The length of the cylinders in Fig is L. L is large such that end effects are negligible (we can treat this as a two-dimensional problem). Torque (T) is required to rotate the inner cylinder at constant speed. Showing all your work and algebra, generate an approximate expression of T as a function of the other variables.
For liquid viscosity measurement, it is desired to create a viscometer consisting of two 30 cm long concentric cylinders. The diameter of the inner cylinder is 20 cm and the diameter of the outer cylinder is 20.2 cm. Since a torque of 0.13 N cinsm is required to rotate the inner cylinder with an angular velocity of 40 rad / s, what will be the viscosity of the fluid in the viscometer in Pa⋅s? Take the value of as 3.
A rotating viscometer consists of two concentriccylinders—an inner cylinder of radius Ri rotating at angularvelocity (rotation rate) vi, and a stationary outer cylinder ofinside radius Ro. In the tiny gap between the two cylindersis the fluid of viscosity m. The length of the cylinders is L. L is large such that end effects are negligible (we can treat this as a two-dimensional problem). Torque (T) is required to rotate the inner cylinder at constant speed. (a) Showing all of your work and algebra, generate an approximate expression for T as a function of the other variables. (b) Explain why your solution is only an approximation. In particular, do you expect the velocity profile in the gap to remain linear as the gap becomes larger and larger (i.e., if the outer radius Ro were to increase, all else staying the same)?
A rotating viscometer consists of two concentric cylinders—a stationary inner cylinder of radius Ri and an outer cylinder of inside radius Ro rotating at angular velocity (rotation rate) vo. In the tiny gap between the two cylinders is the fluid whose viscosity (m) is to be measured. The length of the cylinders is L. L is large such that end effects are negligible (we can treat this as a two-dimensional problem). Torque (T) is required to rotate the inner cylinder at constant speed. Showing all your work and algebra, generate an approximate expression of T as a function of the other variables.
A concentric cylinder viscometer may be formed by rotating the inner member of a pair of closely fitting cylinders. The annular gap is small so that a linear velocity profile will exist in the liquid sample. Consider a viscometer with an inner cylinder diameter of 4 in, a height of 8 in, and a clearance gap width of 0.001 in, filled with castor oil at 90 oF. Determine the torque (in lbf×ft) require to turn the inner cylinder at 400 rpm. The dynamic viscosity of the caster oil is 0.0079 lbf×s /ft2.
Two concentric cylinders are rotating in opposite directions but the same speed, 25 revolutions per minute. The outer cylinder, 11cm in diameter, is turning counterclockwise and the inner cylinder, 10 cm in diameter, is turning clockwise. The gap between the cylinders is filled with a liquid. The liquid is a Newtonian fluid with a viscosity of 0.1 kg/m.s. Both cylinders are 50 cm long. Assuming linear distribution of velocity in the gap, Sketch the velocity profile inside the liquid in the gap At what radial distance from the center of the cylinders the liquid velocity becomes zero? Find the shear rate Find force acting on each cylinder
The device in Fig. is called a cone-plate viscometer. The angle of the cone is very small, so that sin θ ≈ θ ,and the gap is fi lled with the test liquid. The torque M torotate the cone at a rate V is measured. Assuming a linearvelocity profi le in the fl uid fi lm, derive an expression forfl uid viscosity μ as a function of ( M , R , V , θ ).
A cylinder of 125mm radius rotates concentrically inside a fixed cylinder of 130mm radius. Both cylinders are 300mm long. Determine the viscosity (in Pa-s) of the liquid which fills the space between the cylinders if a torque of 0.88 N-m is required to maintain an angular velocity of 2n radians/sec.
Provide detailed explanation: Explain the variation of the viscosity of a fluid withA. TemperatureB. PressureC. DensityD. Temperature & amp; pressureE. Temperature, pressure & amp; density
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A piston with a diameter of 6 cm and a length of L = 13 cm rotates at n = 105 rpm in a cylinder of 6.04 cm in diameter as shown in the figure. Since the dynamic viscosity of the oil between the piston and the cylinder is 1.075 kg · sec · m-2, calculate the moment value that should be applied to the piston rod. M=?
A plate separated by 0.5mm from a fixed moves at 0.50 m/s under a force per unit area of 4.0 N/m². Determine the viscosity of the fluid between the plates.