Question

A cylindrical tank standing upright (with one circular base on the ground) has a radius of 1212 cm for the base. how fast does the water level in the tank drop when the water is being drained at 2323 cm33/sec? note that the volume of a cylinder is v=πr2hv=πr2h where rr is the radius of the base and hh is the height of the cylinder.

Answer 1

The question involves calculating the exit speed of water from a pipe using conservation of energy principles and Bernoulli's equation in the field of fluid mechanics.

Step-by-step explanation:

The question is about the application of the principles of fluid mechanics to determine the speed of water leaving a pipe after being pumped upwards. Using the conservation of energy, specifically applying Bernoulli's equation, we can find the exit speed of water. Here's how to do it:

• First, we calculate the gravitational potential energy gained by the water as it rises 21 meters.
• Then, we find the kinetic energy of water when entering the piston mechanism using its initial speed.
• Considering the work done by the pump and ignoring energy losses, we equate the total initial energy and work done to the final kinetic energy at the exiting point to find the new speed.

Assuming a perfectly efficient system and no loss of energy, Bernoulli's equation gives the exit speed of water after it climbs the 21 meters. However, keep in mind that in real-life scenarios, due to factors like friction and turbulence, the actual speed will likely be slightly lower than the theoretically calculated value.