Final answer:
To calculate the flow rate of water through a hose with a given diameter and velocity, use the formula Q = A × V, where Q is the flow rate, A is the cross-sectional area, and V is the velocity. For a hose of internal diameter 1.60 cm and water velocity 2.00 m/s, the flow rate is approximately 1.2566 L/s.
Step-by-step explanation:
The question relates to the determination of flow rates and velocities in different scenarios involving water motion, representing a typical physics problem in fluid dynamics. Let's break down the problem-solving for one of the examples.
Flow Rate through a Hose
When water is moving at a velocity of 2.00 m/s through a hose with an internal diameter of 1.60 cm, we can find the flow rate as follows:
Flow rate (Q) = Area (A) × Velocity (V)
The internal area can be found using the formula A = πr2, where r is the radius of the hose. First, convert the diameter into radius in meters (1.60 cm is 0.016 m), then find the area:
r = 0.016 m / 2 = 0.008 m
A = π(0.008 m)2 = π(0.000064 m2)
Now calculate the flow rate:
Q = π(0.000064 m2) × 2.00 m/s = 0.0004π m3/s
Convert this to liters per second (1 m3 = 1000 L):
Q = 0.0004π × 1000 L/s = 1.2566 L/s (approximately)