Using Buckingham Pi theorem to find the coefficients of equation: Pi=[density, running speed, diameter, viscosity]=[ρa1, Nb1, Dc1, μ]
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A: Introduction: Viscosity is a measure of a fluid's resistance to flow, which influences how it…
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A: For solution refer below images.
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Q: (2) Referring to the following figure, the distance between plates is Ay = 0.5 cm, Av : 10 cm/s, and…
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A: Data given- u= 500 mm/s = 0.5 m/s y= 1 mm = 0.001 m Shear stress = 0.3 kgf /m2 = 0.3 × 9.81 N/m2…
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A: Given: The shear rate change, du/dy = (50 -10) =40 s-1 The consistency coefficient = 10 Pa.s
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Q: n = Xe)r -Equation 1 vhere X = 1.7419 and (E/R) = -0.018 are constants for a given fluid. You are…
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Q: Can we use the Buckingham pi theorem to prove that the Froud number is dimensionless? Could someone…
A: yes, we use the Buckingham pi theorem to prove that the Froud number is dimensionless
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Q: A capillary tube is being used to measure the viscosity of a Newtonian liquid. The has a 20-mm…
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A: Solution is given below.
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Q: A plate moving 10 cm/s to the right is 0.5 cm above a stagnant wall. The fluid between the plate and…
A: GIVEN DATA- U=10cm/s Viscosity =1.8cp Y=0.5cm we have to find shear stress
Q: An important parameter in fluid flow problems involving thin films is the Weber number (We) which…
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- Viscosity of fluid plays a significant role in the analyses of many fluid dynamics problems. The viscosity of water can be determined from the correlation: H = c, where µ = viscosity (N/s · m²) T = temperature (K) C, = 2.414 × 10-5 C; = 247.8 (K) Cz = 140 (K) What is the appropriate unit for c, if the preceding equation is to be homogeneous in units?Cauchy's ΣF ) equation of motion : pDV/Dt =pg + VT (like pa Newtonian viscous stress relations by the tensor relation : Ti j = - pôij + µ[Əvj/əxi + əvi/axj] where dij is the kroneker delta function (1 for i = T includes pressure and viscous surface forces. into Cauchy's equation, and assume constant viscosity, to get the Navier-Stokes vector eq'ns : pDV/Dt Pg -vp + μ^2 V the acceleration DV/Dt av/at+ (VV)V, which for steady state flow gives DV/Dt =(V.) V. Because (VV) V is a non-linear term on the LHS of the N-S equation Reynolds Number RepVL/μ, a measure of the ratio of inertial to viscous forces. : Patm 10^5 = = N = N = ; pwater 1000; pair 1.2; μwater 10^-3 N s/m^2 ; Hair 2 x 10^-5 N•s/m^2 ; g 9.8 m/s^2 = j; 0 for i j ); NQ1: Apply appropriate solution method using math principles to prove that "the pressure at a point in a fluid has the same magnitude in all directions". Support your answer with sketch. Answer: Px Pz = Pn P are the mean pressures at the three surfaces in the x- and z-directions. Q2: Formulate the issue and identify key variables to prove that [AP = P2 - P, = pg Az = y, Az], where y, and p are the specific weight and density of the fluid, respectively. Az is the vertical distance. Support your answer with sketch. Q3: From fluid mechanics science perspective, define the center of gravity and the center of pressure. Q4: Identify the hydrostatic force acting on the top surface of a submerged rectangular plate by applying principles of engineering for the following cases: 1 tilted plate, (2 vertical plate, and 3 horizontal plate. Support your answer with sketch. Q5: By applying principles of fluid mechanics science, define the "rigid-body" and identify its features. Q6: Formulate the issue…
- A bullet is to be tested in the laboratory to determine the drag force on it. Dependent parameter the drag force D (Newton) depends on the velocity of the bullet V(m/s), the length of the bullet L(m), sound velocity c(m/s), density of fluid ρ (kg/m3) and dynamic viscosity µ(kg/ms). Solve the problem by making the necessary assumptions and drawing the schematic figure. I-Determine the nondimensional p parameters using repeating variables ii-a bullet with a speed of 96,2 m/s in air may be modelled in a water tunnel with a test section velocity of 262 cm/s. Determine the length of the model, if the length of the bullet is 56,2 mm. The air and water temperature is 20 oC degree at 1 atm. iii- if the drag force on the model is measured to be 2,62 N, then determine the expected drag force on the bullet. Comment on dynamic similarity equivalence?Assignment 3 On Viscosity Calculation - Word TOUT REFERENCES MAILINGS REVIEW VIEW Hyperlink P Bookmark tArt Chart Screenshot Apps for Office Online Video Cross-reference Comment Header Footer Page Number Text Quick WordA Box Parts - ns Apps Media Links Comments Header & Footer (2) Referring to the following figure, the distance between plates is Ay = 0.5 cm, Av: = 10 cm/s, and the fluid is ethanol at 273 K having a viscosity of 1.77cp (0.0177 g/cm s). (a) Calculate the shear stress ty and the velocity (b) gradient of shear rate -/dy using cgs units. (c) Repeat using SI units. A Torce Fdshear berween teoparailel platesIf 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?
- 7. Aflat thin plate is dragged at a constant velocity of 4 m/s on the top of a 5 mm deep liquid layer of viscosity 20 centipoise. If the area of the plate is 1 m² find the drag force. Assume variation of velocity in the liquid to be linear. [Ans. 16 N]Orange JO A O X 91|4 2:26 ch1_introductio.. Shear stress (t) is the resistance per unit area of the upper plate t = R/A=T/A Water responds to shear stress by continuously yielding in angular deformation in the direction of the shear. IThe rate of angular deformation in the fluid, d(8)/dt ,is proportional to the shear Istress, as shown in Figure 1.1. do dt dx ,and v = dy dx Angular deformation (Shear strain), 0 = dt do Rate of shear strain = dt dx dv (Velocity gradient) dy dy dt dv Therefore, to dv T = constant dy dv T = - dy The proportionally constant, u, is called the absolute viscosity of the flyid Example A flat plate of 50 cm² is being pulled over a fixed flat surface at a constant velocity of 45 cm/sec (Figure 1.1). An oil film of unknown viscosity separates the plate and the fixed surface by a distance of 0.1 cm. The force (T) required to pull the plate is measured to be 31.7 N, and the viscosity E of the fluid is constant. Determine the viscosity (absolute). 22 Example A flat…Here are these questions if I could get help with themIf a spherical storage tank holds 40,000 gallons (120,000 liters) of water,what diameter must it have?If a cylindrical storage tank has a 40-foot (12 m) diameter circular 05::=how high must it be to hold 1 million gallons (3 million liters)?If water is moving at a rate of 3.2 ft3/sec (90,000 cc/sec), how manygallons (liters) per minute is this?If the specific gravity of gold is 19.0. what is the weight of a cubic inch(cubic centimeter) of gold? A cubic foot (cubic meter)?
- An important parameter in fluid flow problems involving thin films is the Weber number (We) which can be expressed in equation form as We=[pv^2L/(omega)] where p is the density of the fluid, v is a velocity, L is a length, and (omega) is the surface tension of the fluid. If the Weber number is dimensionless, what are the dimensions of the surface tension (omega)?What is the volume of 92.4 grams of chlorine gas that is at a temperature of 46° C and a pressure of 694 mmHg? (Chlorine, R = 62.4 L- mm Hg/mole K and MW = 70.906 g/ mol) Computation: Show your Solution A lump of ice falls from an airplane as it comes into land. If the ice hits the ground with a vertical speed of 85m/s, what was the height of the plane when the ice fell off? (Assume that friction can be ignored.)You have been moved into the laboratory for the fluid testing for hydraulic devices, where your job is to illustrate the results of a viscosity test on a Newtonian fluid at various temperatures and explain discrepancies after completing the following given data-sheet in Table A. A considerable amount of research has been carried out in an attempt to understand the exact nature of the temperature variation of viscosity. One relatively simple model assumes that the viscosity obeys an 'Arrhenius-like' equation of the form n = Xe(k)r Хе --------Equation 1 where X = 1.7419 and (E/R) = -0.018 are constants for a given fluid. You are required to carry out appropriate calculations on the effect of changes in temperature given in table A by using equation 1 for Ethanol on the viscosity of a fluid. Table A NO Temperature viscocity n T°C cP 10 3 20 30 40 6. 50 7 60 8. 70 2. 4) 5.