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- A differential equation encountered in the vibration of beams is d4ydx4=2D where x = distance measured along the beam; [x]=[L] y = displacement of the beam; [y]=[L] = circular frequency of vibration; []=[T1] = mass of the beam per unit length; []=[ML1] D = bending rigidity of beam; [D]=[FL2] Show that the equation is dimensionally homogeneous. Note that [F]=[MLT2] see Eq. (1.21:).Determine the dimensions of constants A and B far which the following equation is dimensionally homogeneous: F=Akx2sinBxk where F is a force, x is a distance, and k represents stiffness (dimensions: [FL1]).Water at T = 20°C rotates as a rigid body about the z-axis in a spinning cylindrical container. There are no viscous stresses since the water moves as a solid body; thus the Euler equation is appropriate. (We neglect viscous stresses caused by air acting on the water surface.) Integrate the Euler equation to generate an expression for pressure as a function of r and z everywhere in the water. Write an equation for the shape of the free surface (zsurface as a function of r).
- Explain why there is an “extra” term in the Bernoulli equation in a rotating reference frame.In the quadratic equation which is homogeneous,a⋅x2+b⋅x+c=0a⋅x2+b⋅x+c=0xx represents a time, cc represents a linear velocity. What are the dimension of aa and bb?Given: U=Uoer/lsin(r/l) Find the above equation's dimensionless form
- 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)?Liquid biofuel (density= 789 kg/m3) is being pumped from a storage tank through a pipe with 1-inch innerdiameter (ID). The fuel is being pumped at a rate of 3.00 gallons per minute. In this process, what is thekinetic energy transport rate (Ėk) in units of horsepower (hp) and ft•lbf/sec.Engine oil at 60°C rotates as a rigid body about the z-axis in a spinning cylindrical container. There are no viscous stresses since the water moves as a solid body; thus the Euler equation is appropriate. (We neglect viscous stresses caused by air acting on the water surface.) Integrate the Euler equation to generate an expression for pressure as a function of r and z everywhere in the water. Write an equation for the shape of the free surface (zsurface as a function of r). (Hint: P = Patm everywhere on the free surface. The flow is rotationally symmetric about the z-axis.)
- On October 21, 2001, Ian Ashpole of the United Kingdom achieved a record altitude of 3.35 km (11,000 ft) powered by 600 toy balloons filled with helium. Each filled balloon had a radius of about 0.47 m and an estimated mass of 0.32 kg. (a) Estimate the total buoyant force on the 600 balloons. (Enter your answer to at least two decimal places.) kN(b) Estimate the net upward force on all 600 balloons. kN(c) Ashpole parachuted to Earth after the balloons began to burst at the high altitude and the system lost buoyancy. Why did the balloons burst? Atmospheric pressure at this high or low altitude is much lower or higher than at the Earth's surface.Q) A body with a mass of 15 kilograms is moving with a velocity of 3 meters/secand. If a force of 15 N is applied to the body, what its velocity aller 5 socunds? discuss your results please.The Reynold's number of a sphere falling in air is 1E6. If the sphere's radius is 1ft, what is its velocity? Density of air is 0.00234 slug/ft³ and viscosity of air is 3.8E-7 lbf-sec/ft²A. 2.5 ft/sB. 5.1 ft/sC. 40.6 ft/sD. 81.2 ft/s