Discharge lab.. Fluids

Lab Report

Jaime A Gomez

Fluid Mechanics (CE 3603)

Section 0A1

Coefficient of Discharge

03.30.2017

Coefficient of Discharge Lab

Abstract

The laws of conservation of mass tell us that Flow rates may or may not be constant. It is important to understand the coefficient of discharge in order to predict different rates of flow and the specific implications for such scenarios. In this lab we observe and record a water tank emptied through an orifice under strict time intervals and measurements.

Introduction

In order to understand pressure differential we must first consider the law of conservation of volume given by the equation:

Where represents the Area of the Tank, represents the differential of water height with respect to time, and represents outlet flow rate. While the Outlet Flow rate also follows:

Where is the area of the outlet, represents the discharge coefficient, “g” represents the acceleration due to gravity, and “h” represents the height from center of outlet. It is indispensable to understand the effects of discharge coefficients in order to control all sorts of flow control applications. There are also devises created to measure speed and flow such as Fire engine pump flow, Aircraft air speed, and Watercraft water speed. In order to find the differential of water height we must combine both equations as such:

The equation must be treated as a first order differential equation.

Experimental Materials & Methods

Trial 1: 5 Second Intervals

No.	Time (sec)	Head (cm)
		40.3
		38.5
	10	36.9
	15	35.2
	20	33.8
	25	32.2
	30	30.7
	35	29.4
	40	28
10	45	26.9
11	50	25.3
12	55	23.7
13	60	22.4
14	65	21.4
15	70	20.1
16	75	18.9
17	80	17.8
18	85	17
19	90	15.8
20	95	14.6
21	100	13.7
22	105	12.8
23	110	11.4
24	115	10.6
25	120	10
26	125	9.3
27	130	8.4
28	135	7.6
29	140	6.9
30	145	6.2
31	150	5.5
32	155
33	160	4.4
34	165	4.1

Figure 1: Table of results from 5 second intervals

The first experimental method required coordinated effort in order to mark distances onto the tank. The timer started the moment the orifice was exposed and a bucket was driven in order to collect the water that was released by the experimental tank. Marks were made every 5 seconds onto the tank’s decreasing water surface height. The results were the following:

Figure 2: 5 Second Interval Run [] with rate of change lines

The data shows the decrease in height with respect to time and the red lines represent the rate of change at three different instances. It is noticeable that the flow rate decreases as a function of time and that the three locations analyzed. A best fit curve line of y = 0.0007x2 - 0.3361x + 40.231.

Trial 2: 10 Second Intervals

No.	Time (sec)	Head (cm)
		40.2
	10	37.5
	20	34.3
	30	30.4
	40	27.7
	50	25
	60	22.1
	70	19.7
	80	17.5
10	90	15.2
11	100	13.2
12	110	11.1
13	120	9.7
14	130
15	140	6.8
16	150	5.5
17	160	4.3
18	170	3.5
19	180	2.5
20	190
21	200	1.3
22	210

Figure 3: Table of results from 10 Second Interval Run

The second experimental method recorded results every 10 seconds. The results were taken using a stopwatch and coordinated efforts to mark water level marks as water decreased. The results were the following:

Figure 4: 10 Second Interval Run [] with rate of change lines

A similar result occurred using 10-second intervals though with more spaced less detailed outcome. However, with given two result outcomes we may be more confident in our conclusions of our results. A best-fit curve line of

y = 0.0008x2 - 0.351x + 40.55.

Results and Discussion

Trial	Q(t = 0)	Q(t = 80s)	Q(t = 160s)
5 second interval	1164	776	388
10 second intervals	1215	772	329
Theoretical	1177	678	332

Figure 5: Table comparison (numbers in )

The results extracted from the data collected have similar characteristics as the theoretical result but offset slightly. The miscorrelation may be caused by several factors during the data collect or/and the capabilities of excel to provide a fit equation for the results. Perhaps what is more interesting is the greater precision of 10-second intervals in comparison to 5-second intervals. The cause might fall in the manner in which a faster pace intervals might cause a miscorrelation between timer and marker.

Conclusions

Flow rate solely depends on the differential change of pressure
Wider spaced intervals yield better results in predicting flow rate and coefficients of discharge
Maintaining a balanced net flow rate of fluid in and out result in a stable, non-changing volume.
It is important to understand flow rate behavior due to its discharge coefficient to predict or manipulate a liquid’s pressure.

Sample Calculations