A balloon filled with helium (of density PHe = 0.164 kg/m³) has a cube shape and rises through the strato-sphere. Air density is given by p(z) = Pa exp(-9), where pa = 1.225 kg/m³ is the density of air at thesea level, g = 9.81 m/s² is the gravitational acceleration, R = 287.06 J/kg/K is the specific gas constant ofair, and T is the air temperature, which is constant in the stratosphere and equal to 217 K (Note that thisexpression for the atmospheric density is strictly correct only in the isothermal region of the stratosphere.However, please use it for solution to this problem). This balloon is designed so that He and its side lengthh = 30 cm remain constant for all z. The lower surface is located at z and the upper surface at z+h. Derivean expression for the buoyancy force on the balloon and compute the maximum altitude to which the balloonrises in a unit of m.IhHe9

Answered: A balloon filled with helium (of…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Consider a column of a planet's atmosphere. The planet's atmosphere is a compressible ideal gas at rest that obeys the polytropic relation Po %3D 3/2 Po 3/2 where pis pressure and pis density. Here, p, and P, are the values of pressure and density, respectively, at the planet's surface. Take z (altitude) to be positive upward with z=0 at the surface, take R to be the gas constant for the planet's atmosphere, and take g to be the downward acceleration due to gravity. a) Starting from hydrostatic balance and the polytropic relation above, derive an expression for the pressure field, p(z), in terms of the given parameters. Leave all parameters except the polytropic index as algebraic. b) Derive an expression for the density field, p(z), in terms of the given parameters. Leave all parameters except the polytropic index as algebraic. c) Derive an expression for the temperature field, T(z), in terms of the given parameters. Leave all parameters except the polytropic index as algebraic.
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For most gases at standard or near standard conditions, the relationshipamong pressure, density, and temperature is given by the perfect gasequation of state: p = ρRT, where R is the specific gas constant. For airat near standard conditions, R = 287 J/(kg · K) in the International System of Units and R = 1716 ft · lb/(slug · ◦R) in the English Engineering System of Units. Using the above information, consider the following two cases: a. At a given point on the wing of a Boeing 727, the pressure andtemperature of the air are 1.9 × 104 N/m2 and 203 K, respectively.Calculate the density at this point.b. At a point in the test section of a supersonic wind tunnel, the pressureand density of the air are 1058 lb/ft2 and 1.23 × 10−3 slug/ft3,respectively. Calculate the temperature at this point.
A child's balloon is a sphere 0.9 ft in diameter. The balloon is filled with helium (p = 0.014 lbm/ft³). The balloon material weighs 0.007 lbf/ft² of surface area. If the child releases the balloon, how high will it rise in the standard atmosphere? (Neglect expansion of the balloon as it rises.) Z= i ft
The surface tension of a liquid is being measured with a ring as shown in the figure. Thering has an outside diameter of 10 cm and an inside diameter of 9.5 cm. The mass of thering is 10 g. The forcerequired to pull the ring from the liquid is the weight corresponding to a mass of 16 g.What is the surface tension of the liquid (in N/m)?
A balloon filled with helium (of density ρHe = 0.164 kg/m3 ) has a cube shape and rises through the stratosphere. Air density is given by ρ(z) = ρa exp(− gz/ RT), where ρa = 1.225 kg/m3 is the density of air at the sea level, g = 9.81 m/s^2 is the gravitational acceleration, R = 287.06 J/kg/K is the specific gas constant of air, and T is the air temperature, which is constant in the stratosphere and equal to 217 K (Note that this expression for the atmospheric density is strictly correct only in the isothermal region of the stratosphere. However, please use it for solution to this problem). This balloon is designed so that ρHe and its side length h = 30 cm remain constant for all z. The lower surface is located at z and the upper surface at z + h. Derive an expression for the buoyancy force on the balloon and compute the maximum altitude to which the balloon rises in a unit of m.
A horizontal turbulent liquid jet of diameter D and average velocity Vj deflected at the angle by a cane mounted on a cart, this exerting a force on the vane, determine the opposing force needed to keep the plate moving at a constant velocity Vv. Neglect the viscosity and gravity forces.
Q1: An oil pipeline and a 1.3m³ rigid air tank are connected to each other by a manometer, as shown in Fig. If the tank contains 15 kg of air at 80°C, the absolute .pressure in the pipeline 1.3 m3 Air, 80°C Oil SG=2.68 Ir= 75 cm Alt = 20 cm 3D D=4 mm 50° Mercury SG = 13.6
The inclined tube manometer shown in the next figure is used to measure small pressure perturbations (Ap). This manometer is composed of a large tube (diameter (D), area (A)) and a small inclined capillary tube (diameter (d), area (a)) and angle (0). Any small pressure difference will result in fluid displacement (Ah) in the large tube and a significant displacement of the fluid in the capillary at a length (AL.). Ap AL initial level Ap (1) Obtain a relationship between (Ah) and (AL) ! (hint: displaced liquid in large tube is equal to that in the small tube ) (2) What the formula for (z2 – 21) ? (hint : height between level 2 and level 1) (3) Express the pressure (Pz-P1) in terms of (AL, 0, p, g, d, and D) ? (4) At what angle should the manometer be adjusted so that (AL-5 Ah) ?
A volume of 400 cc of air is measured at a pressure of 740 mm Hg absolute and a temperature of 18 ˚C. What will be the volume (in cc) at 760 mm Hg and 0 ˚C?
Q1: An oil pipeline and a 1.3m³ rigid air tank are connected to each other by a manometer, as shown in Fig. If the tank contains 15 kg of air at 80°C, the absolute . .pressure in the pipeline Oil 1.3 m Air, 30°C SG=2.68, It= 75 cm Alt = 20 cm 3D 'D=4 mm 50° Mercury SG = 13.6
In Fig.the tank contains water and immiscibleoil at 20 ° C. What is h in cm if the density of the oil is898 kg/m 3 ?

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