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.
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)