CE 3305 Engineering Fluid Mechanics
Spring 2023 Exercise Set 7

LAST NAME, FIRST NAME

R00000000

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Purpose :

Application of continunity to relate flow area and velocity to volumetric (or mass) flow rate.

Assessment Criteria :

Completion, plausible solutions, use of Excel/JupyterLab or calculator.

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Problem 1.

Figure 1 is a schematic of flow in a rectangular channel that is 1.2 m wide. The velocity distribution measured perpendicular from the channel bottom is shown on the figure.

Figure 1: Channel elevation view

Estimate the discharge in the channel.

# sketch here

# list known quantities

# list unknown quantities

# governing principles

# solution (step-by-step)

# discussion

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Problem 2

Figure 2 is a cross section of a heat exchanger comprised of three circular pipes housed inside a larger circular pipe. The internal diameter of the three smaller pipes is 2.5 cm and the pipe wall thickness is 3 mm. The inside diameter of the larger pipe is 8 cm.

Figure 2: Heat exchanger schematic

If the velocity of the fluid in the region between the smaller pipes and the larger pipe is 10 m/s, what is the discharge in m3/s?

# sketch here

# list known quantities

# list unknown quantities

# governing principles

# solution (step-by-step)

# discussion

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Problem 3

Figure 3 is a schematic a tank with a drain in the bottom that has cross-sectional area of 0.0025 $m^2$ and an inlet line on the side with a cross- sectional area of 0.0025 $m^2$, as shown. The cross-sectional area of the tank is 0.1 $m^2$. The velocity of the liquid flowing out the bottom hole is V = $\sqrt{2 gh}$, where h is the height of the water surface above the outlet.

Figure 3: Surge tank schematic

At an instant in time, the water level in the tank is 1 m and rising at the rate of 0.1 cm/s. The liquid is incompressible. Find the velocity of the liquid through the inlet.

# sketch here

# list known quantities

# list unknown quantities

# governing principles

# solution (step-by-step)

# discussion

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Problem 4.

A pipe with a 2 m diameter carries water with mean section velocity of 4 m/s. What is the volumetric discharge in cubic meters per second?

# sketch here

# list known quantities

# list unknown quantities

# governing principles

# solution (step-by-step)

# discussion

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Problem 5.

Water enters the lock of a ship canal through 180 ports, each port having a 2 ft (0.6 m) by 2 ft (0.6 m) cross section. The lock is 900 ft (274.4 m) long and 105 ft (32.01 m ) wide and 50 ft (15.24 m) deep. The lock is designed so that the water surface in it will rise at a maximum rate of 6 ft/min (1.83 m/min). For this condition, what is the mean section velocity in each port?

# sketch here

# list known quantities

# list unknown quantities

# governing principles

# solution (step-by-step)

# discussion

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