The flow of water through a plumbing system in Gallons per h

The flow of water through a plumbing system in Gallons per hour (GPH) is shown below. Outputs from each plumbing device are equal to the sum of inputs. In this example, assume that all faucets from the sink and garden hose are completely open.

Question 20 5 pts Extra Credit Network Analysis Solve using Gauss-Jordan Elimination: The now of water through a plumbing system in Gallons per hour (GPH) is shown below. Outputs from each plumbing device are equal to the sum of inputs. In this example, assume that all faucets from the sink and garden hose are completely open Pipe 1 Sink Water 250 GP Heater Pump (0) Garden pipe 3 Hose 50 G Solve the plumbing system for Xi 1. 2. 3. 4. where X represents the pipes labeled 1.2.3.4. NOTE: When pipe 1 and 3 are shut off: P 3 0 Negative values should not make sense because the water can only flow in one direction through the pipes in this system Make sure your results make sense: Maximum per Edge: Assuming an input of 250GPH from the pump and that shutting off a pipe at the node will redirect the flow to the remaining open pipes, the maximum for any edge up to nodes 3 and 4 would be 250 GPH. Linear Equations Well Pump P1 P2 Pi 250 Water Heater P2 P4 or P2 P4 Sink P1 P. 100 Garden Hose P3 150 Answer the following questions What is the flow of pipe 2 and 4 when pipe 1 and 3 are shut off? P4 P2 250 P2 0, P4 250 P2 p4 150 P2-250, P4

Solution

Given:

Well pump: P₁ + P₂ + P₃ = 250                      (1)

Pipes 1 & 3 are shut off.

So, P₁ = P₃ = 0.

Ao, from (1):

P₂ = 250.

Also, given:

Water heater : P₂ = P₄.

So, P₄ = 250.

So, the correct answer is:

P4 = P2 = 250.