A balloon is surrounded by a tank of liquid at negative pressure and is con-nected to the atmosphere by a tube of length L and cross-sectional area A(Fig. 7.25). The pressure inside the balloon p oscillates above and belowatmospheric pressure causing small changes in the balloon volume V. Theelasticity of the balloon is characterized by its compliance C, defined byAp = AV/C(a) Derive a second-order differential equation for AV(t), assuming that(i) the pressure differential along the tube accelerates the air in the tubeand is not used to overcome entrance, exit, or tube losses; and (ii) the airdensity p is constant. From the equation, show that the natural frequencyof the system is JA/pLC. AtmosphereLength = L; Cross-sectional area = AAir atpressure pLiquidBalloonFigure 7.25

The pressure inside the balloon is given as, If the pressure is considered as gauge pressure, the…

Answered: A balloon is surrounded by a tank 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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3.19 Water flows downward along a pipe that is inclined at 30° below the horizontal, as shown. Pressure difference PA – PB is due partly to gravity and partly to friction. Derive an algebraic expression for the pressure difference. Evaluate the pressure difference if L = 5 ft and h = 6 in. %3D L A Water 30° B 1. te a Mercury h h 2
I need help with section C D E Thank you
A physics lab Consist of a large bowl attached to wire. Students hold onto one of the wire the whirl the ball around in circles and count the number of rotations per second. One group finds these numbers: ball mass=320g, wire length=1.3m, number of rotations/second=2.5. The wire is made of steel with a diameter of 1mm and a Young’s modulus of 20x10^10 N/m^2. How much does the wire stretch due to the tension on it? Should the students correct their data for the wire stretching?
As shown in Fig. 1.12, a horizontal interface 0-0 exists between two immiscible liquids. The dynamic viscosity of these two liquids are 0.14 Pa sand 0.24 Pa s respectively. The thickness is d1 0.8 mm and d2 1.2 mm respectively. Assuming that the velocity gradient is linear. Find theforce F required to push a bottom area A 1000 cm2 wood board to movewith velocity v0 0.4 m/s along the surface?
The pressure gauge shown in the figure consists of a spring inside a vacuum chamber. The chamber is isolated from the environment by a piston, which is free to move up or down. Vacuum Ambient pressure exerts a force on the piston, which compresses the spring. The spring has a force constant of 1250 N/m, and the piston has a diameter of 12 mm. a) At sea level, where ambient pressure is 1 atm, the spring is compressed by distance x, relative to its relaxed length. Calculate xo. b) Suppose the pressure gauge is lowered into water at a lake. At depth D1 = 4 m, the spring is compressed by distance x, relative to its relaxed length. Calculate x1. b) At depth D2, the spring is compressed by distance x2 = 17.325 mm relative to its relaxed length. Calculate D2.
M T M H₂0 2 blocks in water The figure shows two blocks of wood (A and B) connected by a string in a tank of water. The masses are equal (M 0.5 kg). 75% of block A is under water. The volume of block B is 454 cm^3. (a) Determine the tension force of the string. (b) Determine the density of block A. =
For the piping system shown below, water is flowing from left to right at steady-state and constant temperature. You may assume the flow is frictionless. The pipe diameter is larger in section A than section B. The diameters of sections A and C are the same. If gravitation and frictional effects are negligible, which of the following relationships is true about the static pressure in sections A and B? Pc Ps Flow section A section B section C OPA Pg because pressure decreases as velocity increases at steady-state OPA = Pg because friction is assumed to be negligible
A three wheeled OTV has been designed such that the forces from the wheels and motors are uniform, hence the reaction forces at the point of contact with the upper surface can be modeled as a single vertical reaction support. The platform is a square with side length 200mm and has a thickness of 20mm. Plywood has a density of 0.3 g/cm^3. For the purposes of finding the platform weight, W, ignore any holes in the plywood for motor mounts. Due to a misscommunication in the team, the motor mounts M1, M2, and M3 were not attached symmetrically! The potential consequences of this are a difference in reaction forces at the platform to keep it balanced. This difference in reaction forces will result a different normal force at each wheel, and hence the potential for different traction forces, leading to an inability to drive the OTV straight. Co • F: (-75,-75) F₂: (85, -75) • F3: (15,85) -17.4319 MAT 1.338758 3.18886 7 Top View A coordinate system has been defined, such that middle of the…
Determine the tension, T, in Newtons, in the string, where v= 7 m/s, r= 74 cm, m = 8 kg and | m = 33⁰
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Problem 3: Manometer The sensitivity of the micromanometer shown in the figure below is defined as: H Sen = PL - PR (1) Find the sensitivity of the micromanometer in terms of the densities PA and PB. (5 pts) (2) How can the sensitivity be increased? PA Ü H PB Figure 3: Micromanometer.

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