Final answer:
The pressure gradient needed for water acceleration in a pipe at 5 ft/s² varies with pipe orientation due to gravity: The mcq answer for the speed of water emerging from a pipe with a manually operated plunger is b. 19 m/s, based on the provided information and assuming the continuity equation is valid and the initial velocity of the water is negligible.
Step-by-step explanation:
The pressure gradient needed to accelerate water in a pipe at 5 ft/s² depends on the orientation of the pipe due to the presence of gravitational forces, in addition to the required pressure to overcome inertia. For a horizontal pipe (a), the pressure gradient only needs to account for the acceleration due to the applied force. For a vertical pipe with water flowing upward (b), the pressure gradient must overcome both the inertia of the water and gravity. Conversely, for a vertical pipe with water flowing downward (c), the gravitational force aids the flow, reducing the pressure gradient required. Only inertial force is needed for horizontal flow, while for vertical flow, it must also counteract gravity or be reduced by it for upward and downward flow, respectively.
Example Calculation: Using the concept of the continuity equation and the relationship between flow rate and pressure, we can quantitatively determine the pressure needed in various scenarios, including water flowing through horizontal or vertical pipes, and in situations like a decorative fountain or water emerging from a faucet. Notably, the pressure decreases where the pipe narrows, due to increased fluid velocity, a phenomenon observed in the Venturi effect. Understanding how pressure, potential energy, kinetic energy, and gravitational forces interplay is essential to solve fluid dynamics problems.