Instituto Tecnológico y de Estudios Superiores de MonterreyCampus Puebla

Ingeniería de ControlHugo Gustavo González Hernández

PBL“Hydraulic resistance of a valve at home”

José Luis Arellano Camacho A01323890Rigoberto Bobadilla García A01322649

Patricia Estefany Narvaez Morales A01326683Miguel Ángel Urrutia Vidal A01321476

20 de Febrero del 2015

Problem-based learning (PBL)“Hydraulic resistance of a valve at home”

First Partial

Objective

Find the resistance of a valve at home.

Background

A hydraulic system is a method of applying forces through the pressure fluid. The most important hydraulic principle is the principle of Pascal which postulates that: The force exerted on a liquid is transmitted in the form of pressure over the entire volume of the liquid in all directions.

Flow (volumetric)The flow in a pipe is defined as the amount of fluid volume per unit time.

Q=v∗A

where A is the cross sectional area of the pipe and V the velocity of the liquid.

Continuity equationApplying the principle of conservation of mass flow.

Q 1=Q 2v1∗A1=v 2∗A2

where A is the cross sectional area of the pipe and V the velocity of the liquid.

Bernoulli equationB. E is the energy equation for steady flow through a control volume.

v2

2g+ pγ+z=C

The total height in all sections is constant.

Problem

Considering the following system, we conclude that the best way to solve our problem was to use the law of conservation of mass.

Therefore:

(¿)−(out)=(accumulate)

( ¿t)−( out

t)=( accumulate

t)

q i−qo=C dhdt

q o= 1R∗h

qi− 1R∗h=C dh

dt

c h+ hR

=qi

Applying Laplace:

csh (s )+ 1Rh (s )=qi

h ( s)[cs+ 1R

]=qi

Solving:

h ( s)= qi

cs+1R

We know the value of "c" by the following calculation:

d=55cmh=78cm

c=π∗r2=π∗( .552

)2

c=.237582

Finally:

R=dhdq

=2

Resistence of avalve=2

h ( s)= qi

.2375∗s+12

h (t )=qi (4.211 )∗e−2.105 t

Conclusions

Our conclusion is that a mathematical model of any type of system, in our case a hydraulic system, allows us to understand and interpret their operation. Also allowed us to represent variables that define the input and output of the process of our system, which led us to a set of equations and inequalities to obtain the response and variables to solve our problem.

References

Hugo Gustavo González Hernández. (2013). Sistemas de Control en tiempo continuo y discreto. México: Editorial Digital del Tec de Monterrey.