EML3015C Thermal-Fluid I         Fall 1999

Lab. Assignment #4 Draining Water Tank

Fluid Mechanics concepts reviewed: Extended Bernoulli's equation, mass conservation and minor losses.

Water is draining through a circular hole (0.635 cm dia. ) located at the bottom of a cylindrical container (10.16 cm dia.) as shown below.  The draining process is recorded and selected images of the draining sequence are included at the end of the page.

Task 1: Using concepts of mass conservation and the extended Bernoulli's equation, determine theoretically the water depth as a function of time h=h(t).  Introduce a loss coefficient KL in the "extended" Bernoulli's equation to account for the viscous effect and the kinetic energy loss when water exiting through the hole.

Task 2: From the attached image data, determine the water depth, h (see following figure), as a function of time.  Plot sqrt(h) verse time (t).  Identify whether this relation is a linear one.  If yes, fit a least square line through the data points and determine the loss coefficient KL as you compare the experimentally-determined slope to the theoretical value obtained in task 1.  Discuss your results.  Do you think neglecting the velocity at the free surface when you calculate the jet velocity is a good assumption?  Justify your answer.

Task 3: Use the loss coefficient KL found in task 2 and the kinematic relation in engineering dynamics, determine theoretically the distance, x, where the jet passes through the bottom of the ruler as a function of water depth h.  That is to find x=x(h).

Task 4: Use the image data, determine the distance, x, as a function of the water depth (see following figure).  Plot x verse sqrt(h) to see if the data points behave linearly.  If yes, also fit a least square line through data points to determine the slope and compare the experimentally-determined one to the theoretical value.

 

wpe4.jpg (38482 bytes)

Note: Coordinates shown in the figure represent actual pixels(picture elements) of the bitmap file.

The pixel count can be converted to real physical dimension using the following scales,

Vertical scale: 21.4 pixels for each centimeter

Horizontal scale: 18.6 pixels for each centimeter

Use these specifications for all image data

 

Image Sequence (5 seconds between successive images)


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