Mount Vessel
Can anyone please help me with the problem of gauge?
The reservoir and a pressure gauge shown in Figure 2.34 are mounted on a carousel which rotates at 10rpm. The vessel is filled with a negligible gas density, the manometer fluid is water. What the pressure in the tank? Figure 2.34: http://i65.photobucket.com/albums/h203/KaraLJ218/0223092256.jpg I do not know if the picture is what bothers me or anything, but I have no idea how to solve this problem. Can someone please help?
If it was motionless, then pressure in the tank would be = 4 feet of water. But as it is not, there will be a centrifugal force acting on the water in a direction outward causing the liquid level in the right side of the gauge (open end) upwards. So we must subtract that off. So how do we this? Let's start here. that part of the water is driven by centrifugal force? Imagine. a vertical tube of water around a vertical axis. all as the image without the leftmost pipe and tube .. Horizontal like this … … |……| X | X …|……| | …|……| X | where | is the axis Rotation and | X | is the pipe. And of course assume that the bottom of the tube is sealed. What happens as the rotation system? Well the centrifugal force of the water press against the outside (right-most tube in the drawing above). The water seems to have the "weight" due to the acceleration caused by the rotation. But because the tube is attached to the device, there is no net flow of external fluid. nothing happens .. This is to say now what happens if you add a horizontal tube? …|…….| X | X …|…….| | …|.. …..| X | X …|____| | …______| .. Sorry can not draw very well. In any case, take the tube of the bottom is full of water. that the water will create a presure on the wall straight tube = ρ XGX L.. , where ρ = density of water, g = acceleration due to rotation, L = length of pipe. Thus, the total pressure at the base of the column = pressure due to the horizontal pressure + in the tank. in fact you have to add the pressure due to the height of liquid in the shorter leg, but we'll subtracting it off later anyway, so it can be ignored … ok? continued … P = ρ x L xg .. ρ = density of water = 1 g / cm ³ L = 24 ft – 22 ft 2 ft = g =??? although the mechanics of rotation, you learned that g = a ² = rω … right? and ω is in radians / sec … 1 revolution = 2π radians right? So if we turn 10 rpm, ω = 20π / 60 = π / 3 radians / sec … now .. you will notice that we have two different r think it right? 22 feet from the axis merryground and 24 m from the axis merryground? acceleration is not even these two points. Thus Technically, it should be. You do not know what class he is, but for a little more general chemistry. So I will. I will use the average distance. Then a = 23 feet x 23 feet (π / 3s) ² = 25.2 m / s ² continues … I'll end up with a calculation like this … P = ρ XGX L. … ρ in g / cm ³ g in ft / s ², L in feet .. no? units are a problem here … I could not convert the density lbf ft ³ /, then use to convert Gc, but say only convert everything into SI first to avoid that … ρ = 1 g / cm ³ g = 25.2 m / s ² x (12 in / ft) x (2.54 inches / 1) = 774.2 cm / S ² = L x 2 ft. (12 in. / ft) x (2.54 cm / 1) = 60.96 cm to P = (1 g / cm ³) x (774.2 cm / s ²) x ( within 60.96 cm) = 47,195 g / (cm ² xs) and Let's Get the units in this direction … 47,195 g / (cm ² xs) x (1 kg / 1000 g) x (100 cm / 1 m) = 4720 kg / (ms ²) 4720 kg / (ms ²) x (1 m / 1 m) = (4,720 m kg / (m s ²) = 4 720 N / m = 4,720 Pa … since 1 mmHg = 133.5 Pa and since ft H2O = 1 mm Hg 22.41 … 4720 x Pa (1 mmHg / 133.5 Pa) x (1 ft H2O / 22.41 mm Hg) 1.58 m H2O = ******* ********** Ok? always with me or did I lose? so that 4 ft head = Gas pressure + 1.58 m of water in horizontal pipe. if the gas pressure = 4 ft. – 1.58 = 2.4 m. .. I'll leave the GIS FIGS you. and yes .. you may need consider the atmospheric pressure. so that the surface 2.4 of the head .. gauge ****************************
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