2- The resistance (R) experienced by a partially submerged body depends upon the velocity (u), length of the body (L), dynamic viscosity (µ) and density (p) of the fluid, and gravitational acceleration (g). Obtain a dimensionless expression for (R).
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- The heat flux for stable film boiling on the outside of a horizontal cylinder or sphere of diameter D, in m, is given below. What should be the value of "n", for the equation above to be dimensionally consistent? Use dimensional analysis: q=heat flux, W m² W k = thermal conductivity of vapor, 'm °C hgf - [g kỷ Pv(P₁ − Pv)[hfg + 0.4 Cpv (Ts − Tsat)]] à = Cf MyD (Ts - Tsat) Pv = density of vapor, P₁ = density of liquid,- kg m³ kg 'm³ Cpv = enthalpy of vaporization, kg g = gravitatioinal acceleration, C = experimental constant, dimensionless m J kg °C Ts = surface temperature of the heater, °C Tsat = saturation temperature of vapor, °C kg Hv = viscosity of vapor, ms = specific hear of vapor, (Ts - Tsat)Surface tension is due to uneven molecular attraction between immiscible fluid media and solid surface. Its importance is governed by dimensionless parameter Which of the Inertia force called Weber number given by We = Surface tension force™ following statements are correct? (i) Surface tension becomes important when the length scale L is small such as in ink jet printing, coating of thin film, oxygenation of water by falling rain drops. (ii) 111 Super-hydrophobicity can be achieved by micro/nano texturing of surface such as in lotus leave, butterfly and dragonfly wing. During oil spill in ocean, oil floats and spreads out due to gravity. By conservation of mass, the oil film becomes thinner as it spreads. Finally, the surface tension force becomes important causing the formation of tiny oil droplets. (A) (B) (C) (D) (i) and (ii) (i) and (iii) (ii) and (iii) All of the aboveQ1: 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…
- 1- Find using Buckingham Theorem the relationship of the effect on pressure drop (AP) (M L-¹T2), of the variables d- pipe diameter (L), 1- pipe length (L), p-fluid density (ML-³) μ- Fluid viscosity (ML-¹T-¹) and V- Fluid velocity (L T-¹). - Assume the input power to a pump P (ML T-¹) is depend on Q- Flowrate (L3 T-¹), H-pump head (L), p-fluid density (ML-³) Create a relation by dimensional analysis between the power and other variables by Buckingham Theorem. Assume the input power to a pump P (ML T-¹) is depend on Q- Flowrate (L³ T-¹), H-pump head (L), p- fluid density (M L-³) Create a relation by dimensional analysis between the power and other variables by Rayleigh Method.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)?valg, (21535mm 1.15 The pressure difference, Ap, across a partial blockage in an artery (called a stenosis) is approximated by the equation μV Ap - K. 4 + K.(A-1) pv² = K₂ A s.r to zogy nish190 32\V as bonb dignol a 3 basiy noft where V is the blood velocity, u the blood viscosity (FL-2T), p the blood density (ML), D the artery diameter, Ao the area of the unobstructed artery, and A, the area of the stenosis. Determine the dimensions of the constants K, and K. Would this equation be valid in any system of units?
- 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]The resistance R, to the motion of a completely submerged body depends upon the length of the body L, velocity of flow V, mass density of fluid p and kinematic viscosity of fluid v. By dimensional analysis prove that R = pr* L') VL' = pV?1In the figure given, fluid 2 is carbon tetrachloride and fluid 1 is benzene. If patm = 101.5 kPa, determine the absolute pressure at point A. fluid 1 A T 12 cm Patm fluid 2 35 cm ] LIVE 10 nexxt Reimagine Education. www.dlsl.edu.ph
- Using Laplace equation figure out how higher than atmospheric pressure is the inner pressure in a drop of water of radius 3 mm interfacing air at atmospheric pressure. Water surface tension 0.072 N/m. Atmospheric pressure 1.01x105 Pa.The Reynolds number is a dimensionless group defined for a fluid flowing in a pipe as Re = Duplu where Dis pipe diameter, u is fluid velocity, p is fluid density, and u is fluid viscosity. When the value of the Reynolds number is less than about 2100, the flow is laminarthat is, the fluid flows in smooth streamlines. For Reynolds numbers above 2100, the flow is turbulent, characterized by a great deal of agitation. Liquid methyl ethylketone (MEK) flows through a pipe with an inner diameter of 2.067 inches at an average velocity of 0.48 ft/s. At the fluid temperature of 20°C the density of liquid MEK is 0.805 g/cm? and the viscosity is 0.43 centipoise [1 cP = 1.00 x 10-³ kg/(m-s)]. Without using a calculator, determine whether the flow is laminar or turbulent. Show your calculations.The heat transfer coefficient is a nondimensional parameter which is a function of viscosity ? , specific heat cp (kJ/kg·K), and thermal conductivity k (W/m·K). This nondimensional parameter is expressed as (a) cp/? k (b) k/? cp (c) ? /cpk (d ) ? cp/k (e) cpk/?