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- 5.13 The torque due to the frictional resistance of the oil film between a rotating shaft and its bearing is found to be dependent on the force F normal to the shaft, the speed of rotation N of the shaft, the dynamic viscosity of the oil, and the shaft diameter D. Establish a correlation among these variables by using dimensional analysis.5.19 Suppose that the graph below shows measured values of for air in forced convection over a cylinder of diameter D. plotted on a logarithmic graph of as a function of ReD Pr. Write an appropriate dimensionless correlation for the average Nusselt number for these data and state any limitations to your equation.Fluid mechanics theory The power input P to a centrifugal pump is a function of the volume flow Q, impeller diameter D, rotational rate ω, and the density ρ and viscosity μ of the fluid. Determine the three dimensionless numbers. Use M, L, T as your primary dimensions and ω, ρ and D as repeatingvariables.
- The lift force of an aircraft will be studied in a cryogenic wind tunnel, in which nitrogen at low temperature (183 K) and high pressure (5 atm) is employed as the working fluid. The lift force (F) is known to be a function of the wing span (w), the density of fluid (ρ), the speed of the aircraft (V), the viscosity of fluid (μ), and the speed of sound (c). a. Use dimensional analysis to develop a suitable set of dimensionless terms. data : see pictureIn the quadratic equation which is homogeneous,a⋅x2+b⋅x+c=0a⋅x2+b⋅x+c=0xx represents a time, cc represents a linear velocity. What are the dimension of aa and bb?volumetric strain rate as the rate of increase of volume of a fluid element per unit volume. In Cartesian coordinates we write the volumetric strain rate as 1/ V DV/Dt = ∂u/∂x + ∂?/∂y + ∂w/∂zWrite the primary dimensions of each additive term, and verify that the equation is dimensionally homogeneous. Show all your work.
- If the given Pi is 3.14159 Capillary tube: radius = 0.02 cm; length = 9 cm; pressure = 0.7 mmHg Liquid sample: density = 4 ml; time of flow = 4.5 seconds What is the pressure in MKS unit and CGS unit? What is its viscosity? If the weight is 8.5 g, what is its density? What is its kinematic viscosity? What is its fluidity?Cold water enters a pipe, where it is heated by an external heat source . The inlet and outlet water temperatures are Tin and Tout, respectively. The total rate of heat transfer Q. from the surroundings into the water in the pipe is Q. = m·cp(Tout − Tin) where m . is the mass flow rate of water through the pipe, and cp is the specific heat of the water. Write the primary dimensions of each additive term in the equation, and verify that the equation is dimensionally homogeneous. Show all your work.Consider the following equation. All three of the terms in parentheses are dimensionless groups. Because kC is difficult to determine directly, the other variables are measured and kC is calculated from the given equation. What is the estimated value of kC? What are the units of kC? Show your work. The following values were measured: D = 8.0 mm, DAB = 0.475 cm2/s, μ = 1.12 x 10–3 N-s/m2, ρ = 1.00 x 10–3 g/cm3, v = 15.0 m/s. Note: Given Equation attached below
- Important variables in a particular water machine are: Fluid density (ρ), impeller angular velocity (ω), impeller diameter (D), volume flow rate (), fluid viscosity (µ), head (gH). In fact, (gH) shows the energy that the fluid unit mass receives from or gives to the machine, independent of gravitational acceleration (g). Therefore, gH value is used instead of H. Important sizes in terms of the operation of the water machine are power (P), (gH) and efficiency ( h). Derive dimensionless numbers by typing these two parameters based on the above variables and applying Buckingham's p method (repeating variables method).When small aerosol particles or microorganisms move through air or water, the Reynolds number is very small (Re << 1). Such flows are called creeping flows. The drag on an object in creeping flow is a function only of its speed V, some characteristic length scale L of the object, and fluid viscosity µ. Use dimensional analysis to generate a relationship for the drag force FD as a function of the independent variables.Please solve this problem, Thank you very much! Figure is attached 1. liquids in rotating cylinders rotates as a rigid body and considered at rest. The elevation difference h between the center of the liquid surface and the rim of the liquid surface is a function of angular velocity ?, fluid density ?, gravitational acceleration ?, and radius ?. Use the method of repeating variables to find a dimensionless relationship between the parameters. Show all the steps.