Water flow in pipes

Question 1

Define the type of pressure pipe flow we study in this class

Answer 1

refers to full water flow in closed conduits of circular cross section under s certain pressure gradient

Question 2

What are the 4 factors the describe pipe flow

Answer 2

Cross section
elevation
pressure
mean velocity

Question 3

how do we find the mean velocity (equation)

Answer 3

V = Q/A

Question 4

what is the equation for the cross section of a pipe

Answer 4

A = π/4 D^2

Question 5

What did Reynold determine was the affecting factors to turn laminar flow into turbulent flow

Answer 5

velocity, pipe diameter, and the kinematic viscosity
Re = NR =𝜌VD/u = VD/v
where V is mean velocity
v is kinematic viscosity = u/𝜌

Question 6

For a circular pipe, what is the range of NR for laminar flow

Answer 6

NR <= 2000

Question 7

What is the special way to find the mean velocity in laminar flow

Answer 7

V = Vmax/2
Where Vmax is the center line of velocity in the pipe

Question 8

For a circular pipe, what is the range of NR for transitional flow

Answer 8

2000 < NR < 4000
also called the critical zone

Question 9

For a circular pipe, what is the range of NR for turbulent flow

Answer 9

> = 4000

Question 10

Describe figure 3.2 in the book 2. How does laminar flow vs. turbulent floe look like in pipes?

Answer 10

Laminar: parabolic distribution where the mean velocity is equal to one half times the max center line velocity
Turbulent: Logarithmic distribution, as NR gets larger, the center velocity distribution gets flatter.
We can also say that turbulent velocity distribution is more uniform than laminar distribution near the center of the pipe

Question 11

Under ordinary circumstances, water loses energy as it flows through the pipes. This is caused by

Answer 11

1) friction against the pipe walls
2) viscous dissipation occurring throughout the flow

Question 12

What does wall friction depend on

Answer 12

roughness of the wall material (e) and the shear rate/velocity gradient dv/dr at the wall

Question 13

Higher fiction loss may be expected as the Reynolds number ____________

Answer 13

increases

Question 14

Describe what viscous dissipation is

Answer 14

momentum transfer of water molecules between layers is intensified as the flow becomes more turbulent.

Question 15

rate of energy loss in pipe flow varies as a function of

Answer 15

Reynolds number and the roughness of the pipe wall

Question 16

What is the equation for continuity in pipe flows

Answer 16

A1V1 = A2V2 = Q = constant

Question 17

how do we derive the equation for continuity in pipe flows

Answer 17

1)mass flow rate into CV =𝜌1V1A1
2) mass flow rate out CV = 𝜌2V2A2
3) Net mass flow rate 𝜌1V1A1 = 𝜌2V2A2 (conservation law of mass)
4) for steady incompressible flow the rate of change is 0: 𝜌1V1A1 - 𝜌2V2A2 = 0
5) 𝜌1 - 𝜌2 constant
6) A1V1 = A2V2 = Q = constant

Question 18

What is the momentum equation in pipe flow

Answer 18

∑𝑭 ⃑ = 𝝆𝑸(𝑽𝟐 ⃑ −𝑽𝟏 ⃑ )

Question 19

What is the momentum equation in pipe flow in scalar form in the x-direction

Answer 19

∑𝑭x ⃑ = 𝝆𝑸(𝑽x𝟐 ⃑ −𝑽x𝟏 ⃑ )

Question 20

What are the 3 basics forms that energy appears from water flowing in pipes

Answer 20

1. Potential energy related to the elevation (h)
2. kinetic energy related to the motion (V)
3. Pressure energy related to the Pressure (P)

Question 21

How can we express the potential energy equation in pipe flow

Answer 21

𝝆A1V1gh1 - 𝝆A2V2gh2
where m = 𝝆Q
and 𝝆Qgh = 𝝆AVgh

Question 22

How can we express the kinetic energy equation in pipe flows

Answer 22

mV^2 /2
𝝆QV^2 /2
𝝆A1V1(V1^2 /2) - 𝝆A2V2(V2^2 / 2)

Question 23

How can we express the pressure energy equation in pipe flow

Answer 23

hydrostatic force - pressure force opposing the flow
P1A1V1 - P2A2V2

Question 24

Using all the energy equations, how do we derive the overall energy equation

Answer 24

(ρA1V1gh1−ρA2V2gh2)+(ρA1V1(V1^2)/2 −ρA2V2 (V2^2)/2 )+(𝑃1𝐴1𝑉1−𝑃2𝐴2𝑉2)

Divide by ρgQ, Q = AV and γ=ρg we get

ℎ1+𝑃1/γ+𝑉1^2/2𝑔=ℎ2+𝑃2/γ
+𝑉2^2/2g

Question 25

The sum of _____________, ________________, and the _______________ accounts for 3 different energies contained in a unit weight of water flowing through a particular section of pipe or CV between section

Answer 25

the elevation head, the pressure head, and the velocity head

Question 26

describe the head loss

Answer 26

during the flow between upstream and downstream sections, a certain amount of hydraulic energy is lost because of friction

Question 27

describe how the energy equation changes when we consider head loss

Answer 27

H1 = upstream and H2 = downstream H1 > H2 H1 = H2 + hL

Question 28

What is hL when we have a horizontal pipe of uniform size

Answer 28

hL = (P1 - P2) / y

Question 29

what is hL when we have a uniform size pipe

Answer 29

(P1 - P2) /y = hL +h2-h1

Question 30

what is friction head loss

Answer 30

friction loss in flow is a lot more significant than viscous dissipation. therefore the head loss is equal to the friction head loss. hL = hf

Question 31

what is the equation for the friction head loss

Answer 31

hf = f(L/D) (Vavg^2 / 2g)

Question 32

When we have turbulent flow, the friction factor depends less on _________ and ___________ dominates

Answer 32

Reynolds number (NR) relative roughness(e/D)

Question 33

what are the 4 zones of pipe flow in the moody diagram of friction factors for pipe

Answer 33

1) laminar where ln(f) is a linear function of NR 2) A critical zone where f is uncertain because flow is neither laminar or turbulent 3) a transitional zone where f is a function of NR and e/D 4) turbulent flow where f depends on e/D and is independent of NR

Question 34

How do we find the friction factor f

Answer 34

We find the roughness of the material e in table 3.1 book 2, then get relative roughness e/D Once Nr is also known we can use figure 3.8 to find f of circular pipes