Final answer:
Volume flow rate is key to solving problems related to filling or emptying tanks and calculating pressures in fluid systems. Applying Bernoulli's principle and the formula for time using volume and flow rate helps in finding solutions to physics problems on this topic.
Step-by-step explanation:
When solving problems that involve the flow of liquids through pipes, like those presented, we often use the concept of volume flow rate, which is defined as the volume of fluid that passes through a given surface per unit time. In the context of these questions, the volume flow rate concept is useful for calculating how long it takes to fill or empty tanks and for determining pressures at different points in a system.
To calculate the pressure at a point in a hose after a sump pump (like in question 28), we could apply Bernoulli's principle, considering the changes in height, velocity, and hose diameter, to find the pressure at the desired point.
The equation P + 1/2ρv^2 + ρgh = constant (where P is pressure, ρ is density, v is velocity, g is acceleration due to gravity, and h is height) is used to relate the pressures at two points along the flow.
In the scenario of filling a swimming pool (question 9), we use the formula time = volume / flow rate to estimate how long it would take to fill an 80,000 L pool with a garden hose delivering 60 L/min, or by diverting a river with a much larger flow rate.
These types of questions require understanding of fluid dynamics concepts such as viscosity, laminar flow, and Poiseuille's Law, often covered in high school physics courses or introductory college physics.