Flow Between Tanks

Flow Between Tanks

Hydraulics Laboratory

September 2012

John Walton

Goals:

The goals of this exercise are to a) familiarize the student with application of the energy equation, b) learn to estimate flow rates, and d) compare experimental and measured flows.

Methods:

The experiment consists of an upper reservoir of water and a tube that lets water spout into the air. Students should break up into groups and each group should perform the experiments separately. If the TA can procure enough equipment two groups may work simultaneously.

Experiment a:Put the tube to near the bottom of the upper reservoir. Make sure the tube entrance is not blocked. Point the exit of the tube upwards to form a fountain. Move the exit end higher and lower and observe the changes in the height of the spout/fountain. Place the tube at the top of a lower tank (still exiting into the air). Measure the discharge from the amount of water that accumulates in the lower reservoir.

Experiment b: Repeat experiment (a) after moving the tube in the upper reservoir to near the top of the water.

Experiment c: Repeat experiment (a) but let the lower end of the tube flow into the water at the bottom of the lower reservoir.

Experiment d: Repeat experiment (c) after moving the tube entrance half way up the upper reservoir.

Note: the four experiments above can be modified if one or more of the groups wishes to be creative. Must have TA authorization.

Analysis:

Apply the energy equation to all of the experiments, show your work and list assumptions. Estimate the flow for all of the experiments using the Moody Diagram. Create table comparing measured and calculated flow rates.

Energy Equation:

Put point one at the top of the upper reservoir and point 2 just outside the bottom of the tube. Include the minor loss terms. The energy equation should give:

V=SQRT[2 g z/(f L/D + 2)]

Prove it by showing the steps from energy equation to answer in the lab report.

To solve for the velocity we need to know the friction factor but to know the friction factor we need to have the Reynolds number and to get the Reynolds number we need the velocity – Whoops! Our logic is circular in that we need to velocity to calculate the velocity.

The answer is iteration. Assume a first guess Reynolds number. Usually we take the first guess as the flat portion of the relative roughness curves that is in the fully turbulent flow regime. In this case the plastic tubes are smooth so there is no flat region. How about taking the measured flow velocity as a first guess to the calculated velocity? Good idea!

Iteration scheme:

a)Calculate measured velocity as Q/A

b)Use it to estimate the Reynolds number

Reynolds number gives a friction factor to use in V1=SQRT[2 g z/(f L/D + 2)]

c)The new velocity is used to calculate a new Reynolds number and friction factor

Now we get, using the updated friction factor V2=SQRT[2 g z/(f L/D + 2)]

d)Now keep repeating this until the two velocities come out the same – the iteration has converged.