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The cross sections labeled A and B in case (a) are identical to the corresponding cross sections in case (b). Assume that, in both (a) and (b), a fluid in steady motion flows through A with speed { \upsilon }_{ 1 } and exits the system at B with a speed { \upsilon }_{ 2 }. If the pipe sections are to remain stationary and if the mass flow rate is identical in the two cases, determine whether the magnitude of the horizontal force acting on the pipes due to the water flow in case (a) is smaller than, equal to, or larger than that in case (b). In addition, for both (a) and (b), establish the direction of the force.

Step-by-step

The horizontal force is the same in both cases because the change in horizontal momentum of the fluid is the same in both cases. In both cases the horizontal force acting on the pipes due to the water flow is  directed to the left.

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