# Worksheet: Flow Rate and Continuity

In this worksheet, we will practice calculating the flow rate of a liquid given the dimensions of the channel that it is flowing in.

**Q1: **

The Huka Falls on the Waikato River is one of New Zealand’s most visited natural tourist attractions. On average, the river has a flow rate of about 300,000 L/s. At the gorge, the river narrows to 20 m wide and averages 20 m deep.

What is the average speed of the river in the gorge?

What is the average speed of the water in the river downstream of the falls when it widens to 60 m and its depth increases to an average of 40 m?

**Q2: **

The inside volume of a house is equivalent to that of a rectangular solid 13.0 m wide by 20.0 m long by 2.75 m high. The house is heated by a forced air gas heater. The main uptake air duct of the heater is a cylinder 0.300 m in diameter. What is the average speed of air in the duct if it carries a volume equal to that of the house’s interior every 15 minutes?

**Q11: **

What is the definition of a streamline?

- AA family of curves that track the trajectories of fluid particles.
- BThe locus of points of all the fluid particles that have passed through a given point.
- CA family of curves that are instantaneously tangent to the velocity vector of the flow.
- DA family of curves, which are normal to the velocity vector of the flow.
- EA line tangential to the locus of points of all the fluid particles that have passed through a given point.

**Q15: **

Water emerges vertically downward from a faucet that has a 1.600 cm diameter, moving at a speed of 0.400 m/s. Because of the construction of the faucet, there is no variation in speed across the stream.

What is the flow rate of water from the faucet?

What is the diameter of the water stream at a point 0.200 m vertically below the faucet? Neglect any effects due to surface tension.

**Q18: **

A water pumping station is connected to two pipes of constant diameter, as shown in the
diagram. The pipes are of equal diameter. The water enters the pumping station at a
pressure of 3.0 atm and
a speed of . One pipe drops through a vertical
displacement of 12 m. Use a value of
kg/m^{3} for the density of water through the
pumping station and the pipes.

What is the speed of water leaving the pipe that does not change height?

What is the speed of water leaving the pipe that reduces its height?

**Q19: **

A garden hose with a radius of 2.50 cm is used to fill a bucket, which has a volume of 50 liters, taking 60.0 seconds. An adjustable nozzle is attached to the hose to decrease the diameter of the opening, which increases the speed of the water. The hose is held horizontally, 1.5 meters vertically above level ground, and the nozzle diameter is decreased until water from the hose just reaches a flower bed that is 2.5 meters away, horizontally, from the nozzle.

What is the volume flow rate of the water through the nozzle when the nozzle radius is 2.50 cm?

What is the speed at which the water stream exits the hose when the nozzle radius is 2.50 cm?

At what speed must the water stream exit the hose for water from the hose to just reach the flower bed?

What nozzle diameter is required to produce a water stream that just reaches the flower bed?