Mott [Ref. 49, p. 38] discusses a simple falling-ball viscometer, which we can analyze later in Chap. 7. A small hall of diameter D and density
This result is limited by the requirement that the Reynolds number (
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Fluid Mechanics
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- When a clean glass tube with a diameter of 2 mm is immersed in water at 20 ° C, how many mm will the capillary rise occur in the glass tube? For water at 20 ° C, surface tension is given as 0.073 N / m, density 1000 kg / m3, contact angle 0 ° C and gravitational acceleration 10 m / s2.arrow_forwardA 10-in diameter plunger slides in a 10.006-in diameter cylinder, the annular space being filled with oil having a kinematic viscosity of 0.004 ft²/s and specific gravity of 0.85. If the plunger moves at 0.6 ft/s, find the frictional resistance when 9ft is engaged in the cylinder.arrow_forwardLiquid is pushed through the narrow gap formed between two glass plates. Thedistance between the plates is h and the width of the plate is b . Assuming that theflow is laminar, two-dimensional and fully developed, derive a formula for thelongitudinal pressure gradient in terms of the volumetric flow rate, Q, the fluid viscosityand the distances b and h .In an example the above conditions apply with b = 0.10 m and h = 0.00076 m. Theliquid is glycerine that has an absolute viscosity of 0.96 N s/m². A pressure differenceof 192 kN/m² is applied over a distance of 0.24 m. Calculate the maximum velocity thatoccurs in the centre plane of the gap and the mean velocity.Answer 0.06 m/sarrow_forward
- A solid cone of angle 2θ, mass (m), base radius (r0), and density (ρc), is rotating with angular velocity (w0) on its conical seat. The clearance (h) is filled with oil of viscosity (μ). Neglecting air resistance, determine: a) an expression for the moment (M) as a function of r0, w0,μ,θ, and h. b) an expression for the angular velocity (w) for t≥0 as a function of w0,μ,θ,h, r0,m and t if an external torque is not applied. If the radius of gyration of the cone is 16 cm, determine: c ) the value of the angular momentum and velocity if w0=60RPM,h=0.05mm,θ=30°,μ=0.98cPoise , m=20kg, t=2.0sarrow_forwardProve that the pressure at a point is equal in all directions for a fluid at rest with respect to thestationary Cartesian coordinate system XYZ. Comparatively analyse also the definitions of stress andpressurearrow_forwardIf a stream flowing at velocity U past a body of lengthL causes a force F on the body that depends only on U , L ,and fluid viscosity μ , then F must be proportional to(a) ρUL/μ, (b) ρU2L2, (c) μU/L, (d) μUL, (e) UL/μarrow_forward
- A curved blood vessel has an internal diameter ? = 5 mm and a radius of curvature of ?? = 17 mm. Blood has a density of ρ = 1060 kg/m3 and a viscosity of 3.5 cP, and travels at an average velocity of ? = 1 m/s. a) Comment on the nature of the flow with reference to relevant non-dimensional groups. b) Can the flow be modelled using the Hagen-Poisseuile equation? If not, explain what specific assumptions are invalid. c) The viscosity of blood is measured and is shown in Figure Q2. Consider two long straight blood vessels with steady flow. The diameter of the first vessel is 5 mm and the average velocity is 6 cm/s. The internal diameter of the second vessel is 2.2 mm and the average velocity is 50 cm/s. Which vessel would you expect the Hagen-Poisseiulle equation to be more accurate in? Explain your answer (1-2 sentences).arrow_forwardA nuclear reactor is cooled by liquid sodium. The liquid sodium has the following properties: dynamic viscosity = 0.41 mPa·s, specific heat capacity = 1.2 kJ/kgK, thermal conductivity 82 W/mK. Which of the following statements is correct for this scenario? please explain A The thermal boundary layer is thicker than the hydraulic boundary layer. B Heat is transferred through the fluid more easily than momentum. C The velocity varies significantly from the surface to the thickness of the thermal boundary layer. D The hydraulic boundary layer is thicker than the thermal boundary layer.arrow_forwardA cylinder of mass m slides down from rest in a vertical tube whose inner surface is covered by a viscous oil of film thickness h. If the diameter and height of the cylinder are D and L, respectively, derive an expression for the velocity of the cylinder as a function of time, t. Discuss what will happen as t → ∞. Can this device serve as a viscometer?arrow_forward
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