Centre of Pressure, Venturi Meter and Energy Loss Due to Friction in a Pipeline

Posted: August 26th, 2021

Student’s Name

Instructor’s Name

Course

Date

Assessment Task 3 (Summative): Centre of Pressure, Venturi Meter and Energy Loss Due to Friction in a Pipeline

Experiment: Centre of Pressure

1. Define “Centre of Pressure”

The Centre of pressure refers to the point at which the aggregate action field pressure acts from when exerted on a body, resulting in a force acting from the point (Balachandran 93). The aggregate vector of the force that works at the center of the pressure represents the integrated sectorial pressure field.

• What was the independent variable in this experimental investigation?

The independent variable refers to a variable whose variation does not become dependent on other factors. In this experiment, the independent variable is the friction force (Bansal 102). Varying of the friction force does not depend on any consideration within the experimental model.

• Presentation of raw collected from the experiment

Table 1: experimental results

Test Number	H1 ()	H2 ()	M () KG
1
2
3
4
5
6
7

I = 0.1 (m)

B= 0.075 (m)

R= 0.1 (m)

S = 0.25 (m)

O = 0 degree

XpTHEO = 0.0687 m

XpEXP = 0.0602 m

, where h2 = h1 + 100, h mean = h1 + L/2 and X mean =

h mean	X mean	IC o	A	XpTHEO=x mean +ICO/(AX mean)

MGS = M*G*S

F = ₽*g*h*A

G = mgs/F

Xp = y – (0.1 – h1).

Experiment:  Venturi Meter

• Pressure and velocity head variation between P1 and P2 points

According to Bernoulli’s principle,. Assuming that it is a steady flow, the following equation relates viscous fluid, pressure, velocity and the height of the meter (y);

The horizontal pipe has two sections; point p2 is narrower than point p1. Based on the Bernoulli concept, the continuity equation, in this case, demands that the velocity of the flow at point p2 (narrower section) should be higher than that of point p1 (Bansal 66). Since the pipe is horizontal, it implies that the pipes are of the same height. In this case, the equation can be simplified as follows:

Thus, the variation in pressure head at point p1 and point p2 is a result of kinetic energy, which is higher on the right side than on the left side. Therefore, the Bernoulli Principle only holds if the pressure on the left side is lower than the pressure on the right side. Thus, the difference I pressure causes the velocity to be higher in the narrower sides. By illustration, A1V1 = A2V2 from the tube, implying that v2>v2 =v3 using the continuity principle. Now, y applying the Bernoulli Principle, a comparison of points 1 and 2 is made as follows;

Since the heights are equal, the pgy part of equation cancels out, and the simplified equation is as follows;

. The comparison can be rewritten as follows;

However, according to the continuity equation, v2 > v1. In this case, it implies that the comparison on the right-hand side is a positive one. Thus, the left hand should also be positive, indicating that p1> p2. Hence, the pressure deployed at point 2, where fluid velocity is the highest, is lower than the pressure at point 1.

• Meter Coefficient

The coefficient can be obtained using three main equations, that is, Bernoulli, continuity, and manometer equations. Starting with the Bernoulli equation, from point 1 to 2,

In this case, yg represents the specific weight for the fluid flow, and K is the discharge coefficient of the meter according to the highest velocity, v2. The equation can be rearranged to obtain the following,

From the equation K = (

Experiment: Energy Loss Due to Friction in a Pipeline

• Graphical Determination of Friction Coefficient

Pipe 1

Friction Coefficient = – 98.62

Figure 2: Pipe 2

Friction Coefficient = – 551.34

Figure 3: Pipe 3

Friction Coefficient = – 327.02

Figure 4: Pipe 4

Friction Coefficient = – 8.0 * 10^7

• Ensuring the Results from Pipelines are Comparable

To ensure that the results are comparable, the following factors were considered;

• Using pipes of same quality and length
• Using pipes with similar diameter

Quality implies that the four pipes should have the same level of roughness in their surface to ensure that the friction force applied on fluid flowing the pipes is the same. Similarly, have the same diameter ensures the fluid flow through the pipes is subjected to the same pressure (Balachandran 109). Thus, it would ensure that the results can be compared.

Works Cited

Balachandran, P. Engineering fluid mechanics. India: Prentice-Hall of India, 2013. Print.

Bansal, R. K. A textbook of fluid mechanics and hydraulic machines: (in S.I. units. New Delhi: Laxmi Publications, 2005. Print.

Appendices

Question 6

Pipe 1
Test Number	Quantity Collected	Time Taken (s)	h1(m)	h2(m)	hf (m)	Velocity
1	0.003615	15.34	0.835	0.63	0.205	161.02651
2	0.004167	17.19	0.785	0.615	0.17	213.95762
3	0.004085	20.91	0.725	0.6	0.125	205.61978
4	0.003794	22	0.635	0.545	0.09	177.36806
Pipe 2
Test Number	Quantity Collected	Time Taken (s)	h1(m)	h2(m)	hf (m)	Velocity
1	0.003615	16.34	0.765	0.7	0.065	161.02651
2	0.004107	17.19	0.73	0.68	0.05	207.8405
3	0.004085	20.91	0.68	0.64	0.04	205.61978
4	0.003794	22	0.605	0.575	0.03	177.36806
Pipe 3
Test Number	Quantity Collected	Time Taken (s)	h1(m)	h2(m)	hf (m)	Velocity
1	0.003615	15.34	0.835	0.625	0.21	601.99796
2	0.004167	17.19	0.795	0.62	0.175	799.88107
3	0.004085	20.91	0.725	0.59	0.135	768.71002
4	0.003794	22	0.639	0.545	0.094	663.0909
Pipe 4
Test Number	Quantity Collected	Time Taken (s)	h1(m)	h2(m)	hf (m)	Velocity
1	0.003615	15.34	0.915	0.545	0.37	1.891E-06
2	0.004107	17.19	0.86	0.555	0.305	2.441E-06
3	0.004107	20.91	0.78	0.53	0.25	2.441E-06
4	0.003794	22	0.68	0.505	0.175	2.083E-06