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
- Viscosity can be measured by flow through a thin-bore or capillary tube if the flow rate is low. For length L, (small) diameter D« L, pressure drop Ap, and (low) volume flow rate Q, the formula for viscosity is u = D'Ap/(CLQ), where C is a constant. (a) Verify that C is dimensionless. The following data are for water flowing through a 2-mm-diameter tube which is 1 meter long. The pressure drop is held constant at Ap = 5 kPa. T, °C 10.0 40.0 70.0 Q, L/min 0.091 0.179 0.292 (b) Using proper SI units, determine an average value of C by accounting for the variation with temperature of the viscosity of water.arrow_forwardThe sliding plate viscometer shown below is used to measure the viscosity of a fluid. The top plate is moving to the right with a constant velocity of 10 m s in response to a force of 3 N. The bottom plate is stationary. What is the viscosity of the fluid? Assume a linear velocity distribution.arrow_forwardC1 (a). A lubricating oil having the dynamic viscosity of 0.056 poise and specific gravity of 1.17. Calculate (i) the density of oil in kg/m3, (ii) the weight density of oil in N/m3, (iii) the kinematic viscosity in stokes, and (iv) the specific volume in m3/kg. C1 (b). The capillary effect in a glass tube of 2.8 mm diameter, when immersed in (1) water and (2) mercury are 7.7 mm and -3.5 mm respectively. Calculate the value of surface tension in contact with air for water and mercury in N/m. Take, the contact angle for water =0° and mercury =130°. C1(a). (i).the density of oil in kg/m3 C1(a). (ii) the weight density of oil in N/m3 C1(a). (iii) the kinematic viscosity in stokes C1(a). (iv) the specific volume in m3/kg C1 (b). 1.the value of surface tension (water) in N/m C1 (b). 2. the value of surface tension (mercury) in N/marrow_forward
- C1 (a). A lubricating oil having the dynamic viscosity of 0.058 poise and specific gravity of 1.11. Calculate (i) the density of oil in kg/m3, (ii) the weight density of oil in N/m3,(iii) the kinematic viscosity in stokes, and (iv) the specific volume in m³/kg. C1 (b). The capillary effect in a glass tube of 2.6 mm diameter, when immersed in (1) water and (2) mercury are 7.4 mm and -3.5 mm respectively. Calculate the value of surface tension in contact with air for water and mercury in N/m. Take, the contact angle for water =0° and mercury =130°. C1(a).(i).the density of oil in kg/m3 C1(a). (ii) the weight density of oil in N/m3 C1(a). (iii) the kinematic viscosity in stokes C1(a). (iv) the specific volume in m³/kg C1 (b). 1.the value of surface tension (water) in N/m C1 (b). 2. the value of surface tension (mercury) in N/marrow_forwardVelocity distribution of a fluid in a sliding plate viscometer is used to measure the viscosity of the fluid. The top plate is moving with force (F) with a constant velocity (V) as shown in the Figure below. Force (Ft)= 5 N, Velocity (V) = 10 m/s, Temperature = 100°F. Top plate (Area » Length = 0.1 m and width = 0.05 m spaced by 0.001 m) is moving and the bottom plate is stationary. Determine: The viscosity of the fluid. Which fluid is this? Is this fluid more, or less viscous than water? ● IN FLOW N-Larrow_forwardAt any time, approximately 20 volcanoes are actively erupting on the Earth, and 50–70 volcanoes erupt each year. Over the past 100 years, an average of 850 people have died each year from volcano eruptions. As scientists and engineers study the mechanics of lava flow, accurately predicting the flow rate (velocity) of the lava is critical to saving lives after an eruption. Jeffrey’s equation captures the relationship between flow rate and viscosity as: where ρ is the density of the lava, g is gravity, t is the flow thickness, α is the slope, and m is the lava viscosity. Typical values are given as follows for the flow rate: m= 4x103 kg/(m.s) ±1% ρ= 2.5 g/cm3 ±1% t= 28 cm ±0.5 cm α= 10° ±1 ° g= 9.81 m/s²arrow_forward
- Show that Reynold number, pud/µ, is non-dimensional. If the discharge Q through an orifice is a function of the diameter d, the pressure difference p, the density p, and the viscosity µ 1/2 1/2 show that Q = C p?d²/p2 where C is some function of the nondimensional group (dp"“p"µ). %3D 1/21/2arrow_forwardAn airplane that has a cross-sectional diameter D = 4 m of the front portion is to fly at a speed of 600 km/hr in air that has a density of 1.1 kg/m and dynamic viscosity of 1.27 x 10 Pa.s. A small size model of scale ratio (1/17) to be tested in a different fluid that has a dynamic viscosity 5 x 105 Pa .s and a density of 500 kg/m2. It is determined that the parameters that are important for this test are: diameter D, density, viscosity, velocity V, the length of the wings L and the drag force F. What must be the speed (m/s) of the model to Choose... ensure dynamical similitude? What must be the corresponding diameter of the model (cm)? Choose.. What is the number/s of dimensionless groups for this problem? Choose...arrow_forwardThe force f (t) as seen is applied to a stationary mechanical system, where k =1,036 N/m, b = 1,013 N-s/m, fi =494 N, f2 =866 N. Calculate x(t) in meter at t =7.7 sec? f(t) (N) f2 x(t) b fi 00 f(t) 1 2 3 k massless platearrow_forward
- The kinematic viscosity of liquid oil is 20 stoke and relative density = 0.85. Find the dynamic viscosity of this liquid oil in Sl and British systems. (1 stoke = 1 cm/s, 1m 3.28 ft, 1ft 30.48 cm and 1kg = 2.2 lb). Choose the correct answer: a- In SI system 25 kg/m.s and in British system 16.6 Ib/ft.s b- In SI System 17 kg/m.s and in British system 1.17 Ib/ft.s c- In Sl system 20 kg/m.s and in British system 8.15 Ib/ft.sarrow_forwardThe pressure drop (Ap) test is carried out using a pipe configuration as illustrated below: Manometer 1 Manometer 2 straight pipe D= 2R R= radius in pipe The pipe data and the flowing fluid are as follows: Pipe: D = 1 cm; L= 100 cm. Fluid: Water, with density (A) = 1000 kg/m"; absolute viscosity (u) = 0.001 kg/im.s); Experimental data is shown as shown in the following table: Task: Ja. Plot the graph of the pressure as a function of the average velocity (V.v). b. Based on the equation for laminar flow in the pipe as follows: Ap = 32VuL, Vavg (m/s) Ap (Pa) 0,001 0,002 0,005 0,01 0,02 0,04 0,06 0,08 0,1 0,12 0,15 0,30 0,62 1,61 3,10 6,10 12,10 20,10 26,00 32,50 38,90 47,20 D Compare the experimental results in the table with the results of calculations using the above equation. Leave a comment. Note: Ap = p1-p2. c. The coefficient of friction (f) in the pipe is formulated as follows: f- 2DAD PL(V.) plot (plot) this distribution of fas a function of the Reynolds number (Re). Re is…arrow_forwardThe company has opted to purchase a new viscometer for you, as such, you are required by topropose two options for new viscometers. Select two viscometers and explain their operation andconstraints. (P3)b. (P4) Given that you achieved the following results with a U-Tube viscometer:Temperature/ C Time / s40 5760 4180 29100 16Calculate the viscosity at each temperature if the calibration constant is 0.511.d. (M2) Illustrate the results on a graph of temperature vs viscosity and give a briefing on what yourresults indicate, identifying the response of the oil to temperature and explaining anydiscrepancies that may have occurred during the testing.e. (D2) From your testing you discovered that you had a Newtonian and Non-Newtonian sample.Explain to your team what the two terms mean with respect to temperature and shear force onboth samples, giving at least one example of each type of fluid.arrow_forward
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