Question

A peristaltic pump delivers a unit flow (Q1) of a highly viscous fluid. The network is depicted in Fig. P9.14. Every pipe section has the same length and diameter. The mass and mechanical energy balance can be simplified to obtain the flows in every pipe. Solve the following system of equations to obtain the flow in every stream.

Q3 + 2Q4 - 2Q2 = 0
Q5 + 2Q6 - 2Q4 = 0
3Q7 - 2Q6 = 0
Q1 = Q2 + Q3
Q3 = Q4 + Q5
Q5 = Q6 + Q7

Answer 1

To solve the given system of equations representing the flow rates in a peristaltic pump, we can rearrange the equations and eliminate variables to form a system of equations with three unknowns. Solving this system will give us the flow rates in every stream.

Step-by-step explanation:

The given system of equations represents the flow rates in different pipes of a peristaltic pump. To solve this system, we can start by rearranging the equations:

1. Q2 = Q1 - Q3
2. Q4 = Q3 - Q5
3. Q6 = Q5 - Q7

Substituting these expressions back into the first equation, we can eliminate Q2 and Q4:

Q3 + 2(Q3 - Q5) - 2(Q1 - Q3) = 0

Simplifying this equation gives us:

3Q3 - 2Q5 - 2Q1 = 0

Similarly, we can substitute the expressions for Q4 and Q6 into the second equation to eliminate Q4 and Q6:

Q5 + 2(Q5 - Q7) - 2(Q3 - Q5) = 0

Simplifying this equation gives us:

3Q5 - 2Q7 - 2Q3 = 0

Finally, we can substitute the expressions for Q5 and Q7 into the third equation to eliminate Q5 and Q7:

3(Q5 - Q7) - 2Q7 = 0

Simplifying this equation gives us:

Q7 = Q5/2

Now, we have three equations with three unknowns (Q3, Q5, Q1). We can solve these equations simultaneously to find the flow rates in every stream.

Answer 2

hello your question has some missing parts attached below is the missing part

answer : Q = A/BQ = 0.5059 0.4941 0.2588 0.2353 0.1412 0.0941

Step-by-step explanation:

Attached below is the detailed solution

resolved using MATLAB to determine the flow in every stream