the inner cylinder to rotate at a constant speed The viscometer has height and the H, ω. width of the gap is quite small compared to either the radius or Because of small h R1 R2. gap, the fluid velocity in the tangential direction may be assumed to vary linearly across V the gap. If the fluid is a Newtonian fluid with constant viscosity develop a formula for the μ, viscosity in terms of the torque speed and the geometric parameters of the viscometer. T, μ ω, Neglecting the effect of bottom surface, the expression for viscosity is given by HINT of viscosity, , so From Newton’s law Now express and in terms of torque and speed and other known quantities. T τ ω Take the velocity of fluid to vary linearly in the gap h. Illustrates the units Q4. i) for an ideal fluid flowing through a nozzle is Bernoulli’s equation . In the International System of Units (SI), the description and units of each term are p = Pressure, N/m2 (lb/ft2) = Density, kg/m3 (lbm/ft3) ρ V = Velocity, m/s (ft/sec) g = Local acceleration of gravity, m/s2 (ft/sec2) z = Elevation above some datum, m (ft) What are the units of the constant? b) The air drag (D) on a baseball thrown by a pitcher at a speed V in still air is given by D = CD S V2 /2, ρ where,
the inner cylinder to rotate at a constant speed ω. The viscometer has height H, and the width of the gap h is quite small compared to either the radius R1 or R2. Because of small gap, the fluid velocity V in the tangential direction may be assumed to vary linearly across the gap. If the fluid is a Newtonian fluid with constant viscosity μ, develop a formula for the viscosity μ in terms of the torque T, speed ω, and the geometric parameters of the viscometer. Neglecting the effect of bottom surface, the expression for viscosity is given by HINT From Newton’s law of viscosity, , so Now express τ and in terms of torque T and speed ω and other known quantities. Take the velocity of fluid to vary linearly in the gap h. Illustrates the units Q4. i) Bernoulli’s equation for an ideal fluid flowing through a nozzle is . In the International System of Units (SI), the description and units of each term are p = Pressure, N/m2 (lb/ft2) ρ = Density, kg/m3 (lbm/ft3) V = Velocity, m/s (ft/sec) g = Local acceleration of gravity, m/s2 (ft/sec2) z = Elevation above some datum, m (ft) What are the units of the constant? b) The air drag (D) on a baseball thrown by a pitcher at a speed V in still air is given by D = CD ρ S V2 /2, where,
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