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A solid cone of angle 24, tase 1,, and denisity p, is rotat- Ing with initial angulár velocity my inside a conical.seat, as shown in Fig. of visconity u. Neglecting air drag, derive an analytical ex- presslon for the cone's angular velocity ) if there is no applied tengue. The clearance h is filled with oil

A solid cone of angle 24, tase 1,, and denisity p, is rotat- Ing with initial angulár velocity my inside a conical.seat, as shown in Fig. of visconity u. Neglecting air drag, derive an analytical ex- presslon for the cone's angular velocity ) if there is no applied tengue. The clearance h is filled with oil

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)
Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)
8th Edition
ISBN:9781305387102
Author:Kreith, Frank; Manglik, Raj M.
Publisher:Kreith, Frank; Manglik, Raj M.
Chapter5: Analysis Of Convection Heat Transfer
Section: Chapter Questions
Problem 5.9P: When a sphere falls freely through a homogeneous fluid, it reaches a terminal velocity at which the...
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is called a cone-plate viscometer A solid cone of angle 2k, base 1, and density p, is rotat- Ing with initial angular velocity my inside a conical.seat, as shown in Fig. of viscosity u. Neglecting air drag, derive an analytical ex- pression for the cone's angular velocity ) if there is no applied tongue. The device in Fig. The angle of the cone is very small, so thiat sin 0 0, and the gap is filled with the test liquid. The torque M to rotate the cone at a rate 1 is measured. Assuming a lin- ear velocity profile in the fluid film, derive an expression for tiuid viscosity u as a tumction of (M, R. S2, 0). The clearance h is filled with nil Bave C co radius a dwit) dt Fluid I manmot 1Inentia Derive an expression for the capillary height change h for a fluid of surface tension Y and contact angle 0 between two vertical parallel plates a distance W apart, as in Fig. . What will li be for water at 20°C if W = 0.5 mm? A thin plate is separated from two fixed plates by very vis- cous liquids , and g, respectively, as in Fig. plate spacings h, and hy are unequal, as shown. The con- tact area is A between the center plate and each fluid. ta) Assuming a linear velocity distribution in cach fluid, derive the force F required to pull the plate at velocity V. (b) Is there a necessary relation between the two viscosi- ties, 4, and a,? The Take Y= 9790 N/m3 5, The belt in Fig. of viscosity u. Assuming a linear velocity profile, develop a simple formula for the belt- drive power P required as a function of (h, L, V, B, µ). Neglect air drag. What power P in watts is required if the belt moves.at 2.5 m/s over SAE 30W oil at 20°C, with L = 2 m, b= 60 cm, and h=3 cm? Take li = 6.29 Kg m- ree í For SAE 30W Ol) moves at steady velocity V and skims the top of a tank of oil moving belt, width b O4 Oil, depth a 6) A disk of radius R rotates at angular velocity N inside an oil container of viscosity u, as in Fig. . Assuming a lincar velocity profile and neglecting shear on the outer disk edges, derive an expres- sion for the viscous torque on the disk, Clearance h 3,
Transcribed Image Text:is called a cone-plate viscometer A solid cone of angle 2k, base 1, and density p, is rotat- Ing with initial angular velocity my inside a conical.seat, as shown in Fig. of viscosity u. Neglecting air drag, derive an analytical ex- pression for the cone's angular velocity ) if there is no applied tongue. The device in Fig. The angle of the cone is very small, so thiat sin 0 0, and the gap is filled with the test liquid. The torque M to rotate the cone at a rate 1 is measured. Assuming a lin- ear velocity profile in the fluid film, derive an expression for tiuid viscosity u as a tumction of (M, R. S2, 0). The clearance h is filled with nil Bave C co radius a dwit) dt Fluid I manmot 1Inentia Derive an expression for the capillary height change h for a fluid of surface tension Y and contact angle 0 between two vertical parallel plates a distance W apart, as in Fig. . What will li be for water at 20°C if W = 0.5 mm? A thin plate is separated from two fixed plates by very vis- cous liquids , and g, respectively, as in Fig. plate spacings h, and hy are unequal, as shown. The con- tact area is A between the center plate and each fluid. ta) Assuming a linear velocity distribution in cach fluid, derive the force F required to pull the plate at velocity V. (b) Is there a necessary relation between the two viscosi- ties, 4, and a,? The Take Y= 9790 N/m3 5, The belt in Fig. of viscosity u. Assuming a linear velocity profile, develop a simple formula for the belt- drive power P required as a function of (h, L, V, B, µ). Neglect air drag. What power P in watts is required if the belt moves.at 2.5 m/s over SAE 30W oil at 20°C, with L = 2 m, b= 60 cm, and h=3 cm? Take li = 6.29 Kg m- ree í For SAE 30W Ol) moves at steady velocity V and skims the top of a tank of oil moving belt, width b O4 Oil, depth a 6) A disk of radius R rotates at angular velocity N inside an oil container of viscosity u, as in Fig. . Assuming a lincar velocity profile and neglecting shear on the outer disk edges, derive an expres- sion for the viscous torque on the disk, Clearance h 3,
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