The project will involve determining the roots of a virial equation of state with cubic order dependency on specific volume. This program can be used in the future for helping to….

## demonstrate the fluid mechanics using different types of fluids that have different viscosity, tubes of various lengths and diameter, and Develop a model to predict the time the fluid takes to drain to a receiver tank.

Effect Varying Length and Diameter of Exiting Pipes for Tank Draining

Jassim Alajmi

April 29, 2019

Jassim Alajmi, Ashraf Al Shekaili, David Luong, and Siwanet Ratanasiripornchai

Dr. Sergio Mendez

California State University-Long Beach

Department of Chemical Engineering

**Abstract**

The results of draining a tank experimentally without depending on a mechanical device such as pumps. Gravity as a driving force is used to allow fluids in a tank to drain into a receiver tank. The main objective is to experimentally demonstrate the fluid mechanics using different types of fluids that have different viscosity, tubes of various lengths and diameter, and Develop a model to predict the time the fluid takes to drain to a receiver tank. The experimental apparatus consist of a tank, various of pipes, and pressure sensor device which transmit an electric signal to a computer .

**Introduction**

Tank drainage is a process of delivering fluids from one location to the other it could be either by a mechanical device such as a pump or gravity. Fluid from a tank is allowed to drain to a receiver typically located below. Gravity drainage process is comprised of two tanks one with an opening at the bottom that allows the fluid to flow freely out through the hole in the bottom of the upper tank to feed the lower tank. The required background information was Fluid mechanics in order to perform this lab successfully.

Tank drainage is applied in such applications as toilet flushing, rainwater tank as well as in industrial settings. water sources such as the ones used agricultural, household, recreations and also industries.

Bernoulli’s equation was derived to determine the theoretical draining time and compare it with the experimental time. V1= 0m/s and P1=P2 was assumed to determine the draining time. The slope was needed to determine the friction factor that been used to determine the velocity which is at the exit that been used to determine the theoretical time. The following is the equation that been used in this experiment :

(Eq- 1)

We cross out because is equal to zero, and we cross out and because we assumed . After that we solve for which is and the result will be the following:

(Eq- 2)

After that we let a to be the following:

(Eq-3)

After that we did the integration for (Eq-2) and we got the following:

(Eq- 4) we plotted (Eq- 4) in order to get the slope which is and from that we find so that we can plug it in to (Eq-3) in order to get the friction factor . After that we used the friction factor to solve for V in (Eq- 2) which is and we used it in the following equation to find the theoretical time:

(Eq- 5)

Tank drainage consists of draining fluid from a tank whose axis of revolution are vertical, having its top open to the atmosphere, and draining through a small orifice located at the bottom of the tank.

In the experiment fluids with different viscosity, different tube length and diameters were used to collect data that helped compare the draining time with the theoretical model. In the experiment both the total time it takes to drain the tank completely and the draining pattern were measured.

To be able to maintain homogeneity, the experiment was run several times for each of the fluids under the same conditions. These recorded data under the same conditions were used to analyze the difference between observed draining time and the theoretical draining time.

The desired goal of this paper is to present the findings of an experiment in tank drainage without using mechanical pump. The main objective was to experimentally calculate draining time and compare it with the theoretical values for different pipe length and diameter.

**Experimental**

the experimental apparatus consist of a tank, various of pipe in length and diameter, pressure sensor that can read the pressure difference in psi unit. Perform runs with anti-freezing fluid and water separately since they have different viscosity and density.

Figure 1 Figure 2

Figure 1 shows a photo of experimental apparatus with the location of where the outlet pipe can be installed. Figure 2 is a schematic diagram of the experiment that shows the pressure sensor and a computer that it connected to.

The material that been used is a ruler to measure the initial and final level of the fluid. The chemicals that been used in this lab was water and anti-freezing (car coolant)

The following is the experimental steps:

· Fill the tank with a specified amount of fluid for each pipe length

· Record the amount of time that passes for each drain

· Use a computer to measure the gauge pressure at various times

· Apply Bernoulli’s equation for the results to calculate the theoretical time for each drain

· Compare the difference between the actual and theoretical time

· Repeat the procedure for each fluid using different pipes, thoroughly clean the tank and pipes to eliminate chances of contamination

**Results**

figure 3

Figure 4

Figure 5

Figure 6

The tank and the opening are assumed to be at the same pressure. The tank is also assumed to be of sufficiently larger area than the opening so that the friction effects from the tank are negligible. The core of the experiment was the fact that viscosity affects flow rate of fluids more than the shape, length or diameter of the tubes.

Figure 3 shows a plot of the length in inches vs the time in seconds for four trials. The liquid was water and the diameter was constant with changing the length in each run and record the draining time. The experimental is showed in red color where the model is showed in blue. Figure 4 shows also the draining time of water, but with constant diameter and various length with the experimental been in green color and the model in yellow. Figure 5 shows the draining time for anti-freezing fluid with constant diameter and different pipe length. The experimental is been presented in red where the model in blue. Figure 6 also show the draining time of anti-freezing fluid with constant length and different diameter with the experimental been in green color and the model in yellow. Overall, the experimental data was very close to the model, which mean that the model is very good approximation of the draining time. Generally, the water took longer time than the anti-freezing due to the different in the density for the fixed diameter and deferent length.

**Conclusion**

Tank drainage using gravity is an economical way of draining despite the effects of viscosity when using different fluids. It is also important to note that the best system of draining will depend on the area being served. In this experiment we realized with our results that a smaller outlet diameter would take a longer time to drain the fluid, this would be very important when determining the dimensions of the pipe that would provide the desired results. Furthermore, the water took longer time to drain in the fixed length and various diameter trials where the anti-freezing took less time than the water.

**Nomenclature**

h = height of fluid at time, t

L = length of pipe

= frictional factor

V = velocity

*= head loss*

H = total height of tank

D = Diameter

**Reference:**

Dally, J. W., F. Riley, and K. G. McConnell. 1993 Instruments for Engineering Measurements . John Wiley and sons Inc. 2ed.

Streeter, V. L., E. B. Wylie, and K. W. Bedford 1998. Fluid Mechanics. McGraw-Hill, Inc. 8ed.

http://www.Imnoeng.com/tank drainage

Warren L. McCabe, Julian C. Smith and Peter Harriott- Units of Operations Chemical Engineering 7ed

https: //www.wikipedia.org/viscosity