Diagram shown Fluid Mechanics Problem 2. (10 points) Water enters a pipe system

Question

Diagram shown
Fluid Mechanics Problem

2. (10 points) Water enters a pipe system at point 1. The pipe system drops 100 m and then encounters a constriction/expansion in the pipe at point 2, and ultimately exits the pipe system at point 3. Assume 1) the density of the water is constant at 1 g/cm3 2) There is no loss of energy to friction 3) There is no loss of energy at the constriction/expansion (point 2) 4) the flow is laminar and irrotational The known pressures, heights, velocities, and radii of the pipe at points 1, 2 and 3 are included in the diagram below. What is the velocity of the water at point 3? Show your work!

Explanation / Answer

Use bernoulis equation between 1 and 2 and 1 and 3

1 & 3
P_0 + rho*v^2/2 + rho*g*h = constant
202650 + rho*5*5/2 + rho*g*100 = 202650 + rho*v*v/2 + rho*g*100 = constant
there v_3 = 5 m/s

202650 + rho*5*5/2 + rho*g*100 = 101325 + rho*v_2*v_2/2
sqrt(2*(101325/1000 + 25/2 + 980)) = v_2 = 46 m/s

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