Hi!
Ok
P = Po + (greek lowercase letter Ro)gh
pressure = atmospheric pressure + density of fluid(gravity)(pressure head)
I derived it using calculus and followed along in the book the book assuems in ther derivation that it's a solid cylinder that sits straight up and down...
what do I do if say there was a water tank on a clif and instead of the water falling straight down towards a house and went down a pipe that was slanted at an angle say I don't know 45 degrees from the horizontal...
I would i derrive my new equation what other information would I need to know to make the new derivation?
Basicaly instead of assuming a graduated cylinder what if it was like some werid shape how would I derive my new equation?
Could you make up values that i would need and walk me threw the first couple of steps?
Thanks a bunch!!!
like instead of a cube of water what if it was a fish bowl or like a lake not some perfectly shaped cube that contained the water
Certainly! In order to derive the new equation for the water tank scenario you described, you would need to consider the geometry and the forces acting on the system. Here's a step-by-step process to help you derive the new equation:
1. Define the geometry: Determine the shape of the water tank and the slanted pipe. Let's assume for simplicity that the tank is a rectangular prism and the pipe is a straight slanted pipe with an angle of 45 degrees from the horizontal.
2. Identify the forces: Consider the forces acting on the water in the tank and the pipe. The main forces to consider are gravity and the pressure exerted by the water column.
3. Determine the pressure at different points: Divide the system into different sections (e.g., top of the tank, bottom of the tank, entrance of the pipe, exit of the pipe). For each section, calculate the pressure using the equation you provided initially (P = Po + ρgh), where Po is the atmospheric pressure, ρ is the density of the fluid (water in this case), g is the acceleration due to gravity, and h is the height of the fluid column at that point.
4. Consider the slanted pipe: Since the pipe is slanted, you will need to account for its angle. Decompose the gravitational force acting on the water column into two components: one perpendicular to the slanted pipe and one parallel to it. The component parallel to the pipe will affect the pressure.
5. Derive the new equation: Take into account the forces acting on each section and the geometry of the system. You may need to use trigonometry to determine the appropriate components of forces and pressures. By doing so, you can derive the new equation describing the pressure at different points in the system.
I'm unable to provide specific numerical values without further details, but you can start by considering the dimensions of the tank, pipe, and the height of the water column. With these dimensions, you can calculate the pressure at different points in the system using the derived equation.
Remember to verify the derived equation with experimental data or compare it to existing theoretical models if available.