Apply the grid method in solving the following questions to check for dimensional homogeneity. 1. For an atmospheric pressure of 101 kPa (abs) determine the heights of the fluid columns in barometers containing one of the following liquids: (a) mercury (SG = 13.55), (b) water, and (c) ethyl alcohol (SG = 0.79). Do these results support the widespread use of mercury for barometers? Why?
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- Q1: 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…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)For a venturi meter given below, the volumetric flow rate is defined in terms of the geometrical parameters, the density of working fluid (p), and density of the manometer liquid (pm) as 4. Q = f(D, D2, A2, g, h, Pmv Pr) %3D Write down the balance equations and show your work to end up with an expression for the volumetric flow rate in terms of the variables defined above.
- When a liquid in a beaker is stired, whirlpool will form and there will be an elevation difference h, between the center of the liquid surface and the rim of the liquid surface. Apply the method of repeating variables to generate a dimensional relationship for elevation difference (h), angular velocity (@) of the whirlpool, fluid density (p). gravitational acceleration (2), and radius (R) of the container. Take o. pand R as the repeating variables.Taylor number (Ta) is used here to describe the ratio between the inertia effect andthe viscous effect. By applying Buckingham Pi’s Theorem, determine an equation forTa as a function of the radius of inner cylinder (r), cylinder tangential velocity (v),fluid dynamic viscosity (μ), gap distance (L) and fluid density (ρ).The mass of a flid stem is 0.311 slu, ts density is 30 l/ft' and the force of gravityis at 31.90 fps". Fin (a) the secfic olume in cm'/g,(b) the specfic weight ke/m', and (c) the total volume in in'. Solve the following problems SYSTEMATICALLY, enclose your final answers in a box, and Please write clearly. Thanks.
- 1. A special-purpose piece of laboratory glassware, called a pyncnometer; is used to measureLiquid densities. It has a volume of 25 cc, and a mass of 17 .24 g when it is full of air. Whenfilled with a liquid of unknown density, its mass = 45.00 g. What is the density of this liquid?How large an error do we make if we ignore the mass of the air that was in it when we weighed itand found m = 17.24 g?In the following section, at least 2 to up to 5 answers may be correct. 1) For a fluid, the assumption (simplifying notion) of incompressibility has important consequences: Pascal’s principle: a change of pressure in an enclosed fluid at rest is transmitted undiminished to all points in the fluid. pressure changes are transmitted immediately from one place to another. the speed of sound then is infinite (just within this approximation). pressure becomes unpredictable. none of the above. 2) Archimedes’ principle can be summarized as: an immersed object is buoyed up by a force equal to the weight of the fluid it displaces. a bathtub is fun, and may lead to important physical discoveries regarding the volume of an object and how much water it displaces, and the weight of that amount of water. boats swim because of the work done by sailors. submarines are always doomed. fish swim because they are less heavy than water 3) A…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)?
- b) When a liquid in a beaker is stirred, whirlpool will form and there will be an elevation difference h, between the center of the liquid surface and the rim of the liquid surface. Apply the method of repeating variables to generate a dimensional relationship for elevation difference (h), angular velocity (o) of the whirlpool, fluid density (p), gravitational acceleration (g), and radius (R) of the container. Take o, p and R as the repeating variables.In Figure below all fluids are at 20 deg.C. Determine pressure at point B, if pressure at point A is 150 kPa and weight of air is neglected. Use the table below for the densities at 20 deg.C. Liquid p. kg/m Kerosene - Ammonia 608 Benzene 881 Air Carbon tetrachloride 1590 Benzene Ethanol 789 Ethylene glycol Freon 12 B 1117 40 cm 9 cm 1327 20 cm Gasoline 680 14 cm Glycerin Kerosene 1260 t8 cm 804 Mercury- Water Mercury Methanol 13,550 791 SAE 10W oil 870 SAE 10W30 oil 876 SAE 30W oil 891 SAE 50W oil 902 Water 998 Seawater (30%e) 1025The density of liquid water at 25 degrees celsius equals 62.2lbs/cube ft. Suppose the KD DF stud at the top of the page weighs 13.35lbs. And suppose the KD DF stud is thrown into a swimming pool, Twater=25 degrees celsius. Based on data would the stud: sink completely, partually. or float completely