Calculating Water Flow With Known Velocity at One End

• 1). Convert all your measurements to SI units (the agreed-upon international system of measurement). Convert pressure to Pa, density to kg/m^3, height to m, and velocity to m/s. You can find conversion tables online (see Resources section).
  
  
• 2). Solve Bernoulli's equation for the desired velocity, either the initial velocity into the pipe or the final velocity out of the pipe.
  
  Bernoulli's equation is P_1 + 0.5*p*(v_1)^2 + p*g*(y_1) = P_2 + 0.5*p*(v_2)^2 + p*g*y_2 where P_1 and P_2 are initial and final pressures, respectively, p is the density of the water, v_1 and v_2 are initial and final velocities, respectively, and y_1 and y_2 are initial and final heights, respectively. Each height is measured from the center of the pipe.
  
  To find the initial water flow, solve for v_1. Subtract P_1 and p*g*y_1 from both sides, then divide by 0.5*p. Now take the square root of both sides to obtain the equation v_1 = { [P_2 + 0.5*p*(v_2)^2 + p*g*y_2 - P_1 - p*g*y_1] / (0.5*p) }^0.5
  
  Perform an analogous calculation to find final water flow.
  
  
• 3). Substitute your measurements for each variable (the density of water is 1,000 kg/m^3), and calculate the initial or final water flow in units of m/s.
  
  

Calculating Water Flow With Unknown Velocity at Both Ends

• 1). If both v_1 and v_2 in Bernoulli's equation are unknown, use conservation of mass to substitute v_1 = v_2*A_2 / A_1 or v_2 = v_1*A_1 / A_2 where A_1 and A_2 are initial and final cross-sectional areas, respectively (measured in m^2).
  
  
• 2). Solve for v_1 (or v_2) in Bernoulli's equation. To find initial water flow, subtract P_1, 0.5*p*(v_1*A_1 / A_2)^2, and p*g*y_1 from both sides. Divide by [0.5*p - 0.5*p*(A_1 / A_2)^2]. Now take the square root of both sides to obtain the equation v_1 = { [P_2 + p*g*y_2 - P_1 - p*g*y_1] / [0.5*p - 0.5*p*(A_1 / A_2)^2] }^0.5
  
  Perform an analogous calculation to find final water flow.
  
  
• 3). Substitute your measurements for each variable, and calculate the initial or final water flow in units of m/s.