Homogeneous equilibrium model-fluid flow

[Sivaraman]

Hello,I am trying to calculate the velocity in a pipe with length L and Dia D, which is connected to bottom of a pressurized vessel (Vessel dimensions are known, Level of liquid inside the vessel is known).
Now i need to figure out the velocity as a function of pressure inside the vessel.We can ignore the friction losses in the pipe, and the vessel is filled with water. Thank you

 

[Illmatic1]

.The velocity through the pipe can be calculated using Bernoulli’s equation. The equation states that when a fluid flows through a pipe with no losses (frictionless), the sum of its pressure, kinetic energy and potential energy will remain constant. This means that the pressure at the start of the pipe (pressure at the bottom of the vessel) is equal to the pressure at the end of the pipe, minus the kinetic and potential energy of the flow.The equation can be written as:P1 + (V1^2 / 2g) + z1 = P2 + (V2^2 / 2g) + z2where P1 and P2 are the pressure at the start and end of the pipe respectively, V1 and V2 are the velocities at the start and end of the pipe respectively, g is the acceleration due to gravity, and z1 and z2 are the elevation at the start and end of the pipe respectively.Since z1 and z2 are zero in this case, the equation simplifies to:P1 + (V1^2 / 2g) = P2 + (V2^2 / 2g) Rearranging the equation, we can calculate V2 (velocity at the end of the pipe) as:V2 = sqrt(2g * (P1 - P2)) where P1 is the pressure at the bottom of the vessel, and P2 is the pressure at the end of the pipe.