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A saltwater solution at a concentration of 6 g/m^3 enters a 25 m^3 tank at a flow rate of 0.5 m^3/min. The uniformly mixed solution leaves the tank at a flow rate of 0.25 m^3/min.

User Sakiboy
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Final answer:

The student's question involves using principles of fluid dynamics within physics to calculate hydrostatic pressure, flow rate changes, and the conditions for flow direction reversal in a saline solution IV system.

Step-by-step explanation:

The student's question deals with fluid mechanics, a branch of physics that involves the study of fluids (liquids, gases, and plasmas) and the forces on them. Specifically, the question is about hydrostatic pressure in a saline solution IV system, flow rate changes with varying solution heights, and the reversal of flow direction, all of which fall under the high school level fluid dynamics curriculum.

(a) To verify the pressure at a depth of 1.61 m in a saline solution assuming its density to be that of seawater, you can use the hydrostatic pressure equation P = ρgh, where ρ represents the density of sea water, g is the acceleration due to gravity (9.81 m/s2), and h is the depth of the fluid. Using the given density for seawater, you can calculate the expected pressure.

(b) The new flow rate when the height of the saline solution is decreased to 1.50 m can be calculated using the principle that flow rate is proportional to the square root of the hydrostatic pressure (flow rate is proportional to √(P)), meaning that when the height decreases, the flow rate will also decrease.

(c) The height at which the direction of flow reverses can be determined by finding the condition where the hydrostatic pressure due to the saline solution's weight is equal to the venous pressure opposing the flow. Below this height, the direction of flow will reverse.

User Ben Reynwar
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