A spherical tank is used for storing water. The tank is filled through a hole in the top and drained through a hole in the bottom. If the tanks radius is r, you can use integration to show that the volume of water in the tank as a function of its height h is given by:
please solve only with matlab code
A spherical tank is used for storing water.The tank is filled through a hole in the top and drained through a hole in the bottom. If the tank's radius is r, you can use integration to show that the volume of water in the tank as a function of its height h is given by: (Eq.1) Torricelli's principle states that the liquid flow rate through the hole is proportional to the square root off the height h. Further studies in fluid mechanics have identified the relation more precisely, and the result is that the volume flow rate through the hole is given by: CdA, V2gh (Eq. 2) Where A is the area of the hole, gis the acceleration due to gravity, and Cais an experimentally determined value that depends partly on the type ofliquid. For water, Ca 0.6 is a common value. We can use the principle of conservation of mass to obtain a differential equation for the height h. Applied to this tank, the principle says that the rate of change of liquid volume inthe tank must equal the flow rate out of the tank; that is: (Eq. 3) From Eq.1, dV dh dh dh. nh nh(2r -h) dt dt dt Substituting this and Eq.2 into Eq.3 gives the required equation for h. dh. (Eq.4) Use MATLAB to solve the equation to determine how long it will take for the tank to empty if the initial height is 5ft. The tank has a radius ofr-3ft and has a 0.5in diameter hole in the bottom. Use g 32.2 ft/seca. Check your solution. A spherical tank is used for storing water.The tank is filled through a hole in the top and drained through a hole in the bottom. If the tank's radius is r, you can use integration to show that the volume of water in the tank as a function of its height h is given by: (Eq.1) Torricelli's principle states that the liquid flow rate through the hole is proportional to the square root off the height h. Further studies in fluid mechanics have identified the relation more precisely, and the result is that the volume flow rate through the hole is given by: CdA, V2gh (Eq. 2) Where A is the area of the hole, gis the acceleration due to gravity, and Cais an experimentally determined value that depends partly on the type ofliquid. For water, Ca 0.6 is a common value. We can use the principle of conservation of mass to obtain a differential equation for the height h. Applied to this tank, the principle says that the rate of change of liquid volume inthe tank must equal the flow rate out of the tank; that is: (Eq. 3) From Eq.1, dV dh dh dh. nh nh(2r -h) dt dt dt Substituting this and Eq.2 into Eq.3 gives the required equation for h. dh. (Eq.4) Use MATLAB to solve the equation to determine how long it will take for the tank to empty if the initial height is 5ft. The tank has a radius ofr-3ft and has a 0.5in diameter hole in the bottom. Use g 32.2 ft/seca. Check your solution
