A system (8) is provided for weighing and monitoring flow from multiple fluid sources (76) into a flow system (10) wherein incoming fluid is received in a weighing bag (80) att- ached to a control system for monitoring the amount of fluid passed through the weighing bag (80) and for preventing admis- sion of air into the flow system (10). An alarm attached to the weighing bag (80) warns when fluid in the weighing bag (80) is approaching empty, so that the fluid in the weighing bag (80) can be replenished from the fluid source (76) before the weigh- ing bag (80) runs dry. If fluid in the weighing bag (80) is not re- plenished, the system automatically shuts down. The fluid pump (72) can be absolutely calibrated using the controlled admission of known amounts of fluids into the weighing bag (80) so that the amount of fluid introduced into the flow system (10) through the weighing bag (80) can be calculated automatically.