What is Betz limit ? Derive an expression for it !

Suppose a aluminum rod of 20 ft and solid square cross section of 0.5 inches, isfixed at a wall on the left end. On the right end it is unsupported. The rod will bendbased on it’s own weight given that it has uniform density.a.) Find the Youngs modulus, Moment of Inertia, and Weight per unit necessary tosolve this problem. Then put them together to find the coefficient on the x4term.b.) Solve for coefficients c1 through c4 and report the equation governing the shapethis rod will take.c.) How far down from level does the end of the aluminum rod hang in inches?

An open cylindrical container containing liquid is spinning about its vertical axis such that the liquid undergoes rigid body rotation. Which of the following phenomena are correct? (1) The surface of the liquid is a curve with lowest point at the axis of rotation. There will be no shear stress. There will be no pressure stress. (iii) (A) (B) (C) (D) (i) and (ii) (i) and (iii) (ii) and (iii) All of the above The Energy Line (EL) and Hydraulic Gradient Line (HGL) are used to represent the condition in a pipe flow. Which of the following statements are correct? (1) The difference between EL and HGL is the velocity head. When Bernoulli equation is valid, the EL is constant and remains horizontal, but the HGL needs not necessary so. When there is a sudden contraction in the pipe flow, the HGL will drop. (A) (B) (C) (D) (i) and (ii) (i) and (iii) (ii) and (iii) All of the above

a box with a mass 20kg its been pull with a force constant P=W of the box was in constant repose what is the velocity after the box reach a distance of 2m, with a coheficient mk=0.2

..P15 A horizontal cylinder 10 cm in diameter contains helium gas at room temperature and atmospheric pressure. A piston keeps the gas inside a region of the cylinder 20 cm long. (a) If you quickly pull the piston outward a distance of 12 cm, what is the approximate temperature of the helium immediately afterward? What approximations did you make? (b) How much work did you do, including sign? (Note that you need to consider the outside air as well as the inside helium in calculating the amount of work you do.) (c) Immediately after the pull, what force must you exert on the piston to hold it in position (with the helium enclosed in a volume that is 20 + 12 = 32 cm long)? (d) You wait while the helium slowly returns to room temperature, maintaining the piston at its current location. After this wait, what force must you exert to hold the piston in position? (e) Next, you very slowly allow the piston to move back into the cylinder, stopping when the region of helium gas is 25 cm long.…

What do differential and integral analyses of kinetic data entail? Which is more precise and why?

hat is Reynold’s equation of motion? Explain capillarity and pitot tube.

A cube of side (a) and mass (M) is initially sitting fully submerged at the bottom of a container filled with a liquid of kinematic viscosity v and density p. The container has a square cross-section of side (a+a/5) and the cube is sitting right at the middle of the container base. (a) A force (F) starts pulling the cube up at a constant velocity (U). Develop an expression for the force in terms of (U, M. a. g, p and v). You may assume that the velocity in the gap between the cube's sides and the container walls is linear. The expression for (F) is to be valid as long as the cube remains submerged. (b) After the cube reaches the water surface, it continues to be pulled up by the same force. Develop a differential equation for the variation with time of the fraction of the cube that is submerged in water.

6. Beginning with the equations on page 3, show the detailed steps needed to obtain the equation on p. 8.