Gauge pressure/flow velocity

In summary, the conversation is about calculating the flow velocity and gauge pressure of water at different points in a pipe system. The equation used is Bernoulli's equation and there is a mistake in the units used for one of the calculations. The correct flow velocity on the top floor is 3.450887574 m/s and the correct gauge pressure is 1.990429541 atm.
  • #1
Stryder_SW
23
0
1. Homework Statement
Water at a gauge pressure of 3.8 atm at street level flows into an office building at a speed of 0.80 m/s through a pipe 5.4 cm in diameter. The pipe tapers down to 2.6 cm in diameter by the top floor, 20 m above (see figure here http://www.uploadgeek.com/share-85DD_49B54943.html [Broken]). Assume no branch pipes and ignore viscosity.
A). Calculate the flow velocity in the pipe on the top floor.
I have this, its 3.450887574 m/s

B).Calculate the gauge pressure in the pipe on the top floor.
*****Figured it out, I wasn't tracking units.*****

2. Homework Equations
I have been trying to use Bernoulli's equation. P1+(.5 pv12)+(pgy1) = P2+(.5 pv22)+(pgy2)

3. The Attempt at a Solution
So far solving for P2 in Bernoulli's equation and dividing by 101300(pa/atm). I have come up with 1.990429541 atm. for my answer. Unfortunately this is wrong, help would be greatly appreciated.
 
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  • #2
So far solving for P2 in Bernoulli's equation and dividing by 101300(pa/atm). I have come up with 1.990429541 atm. for my answer. Unfortunately this is wrong, help would be greatly appreciate

Show your calculations.
 
  • #3


I would like to clarify a few points before providing a response. First, gauge pressure is the pressure measured relative to atmospheric pressure, so it is important to specify the reference point for the given gauge pressure of 3.8 atm. Second, the units for flow velocity should be in meters per second (m/s) rather than meters per hour (m/h). Finally, it is important to state the assumptions made in the problem, such as the fluid being incompressible and the flow being steady and laminar.

With these clarifications in mind, let's proceed with the solution. Bernoulli's equation is a valid approach to solving this problem. We can write it as P1 + (0.5 * ρ * v1^2) + (ρ * g * y1) = P2 + (0.5 * ρ * v2^2) + (ρ * g * y2), where P is pressure, ρ is density, v is velocity, g is acceleration due to gravity, and y is height.

For part A, we can use the given information to solve for v2, the flow velocity on the top floor. Plugging in the values, we get:

P1 = 3.8 atm
v1 = 0.80 m/s
d1 = 5.4 cm = 0.054 m
d2 = 2.6 cm = 0.026 m
y1 = 0 m
y2 = 20 m

ρ is the same for both points, so it cancels out. Solving for v2, we get:

v2 = 0.80 * (d1/d2)^2 = 3.45 m/s

For part B, we can use the same equation to solve for P2, the gauge pressure on the top floor. Plugging in the values, we get:

P1 = 3.8 atm
v1 = 0.80 m/s
v2 = 3.45 m/s
d1 = 5.4 cm = 0.054 m
d2 = 2.6 cm = 0.026 m
y1 = 0 m
y2 = 20 m

ρ is still cancelled out, so we are left with:

P2 = 3.8 + (0.5 * 0.80^2) -
 

1. What is gauge pressure and how is it different from absolute pressure?

Gauge pressure is the pressure measured relative to atmospheric pressure. It is the difference between the total pressure (absolute pressure) and the atmospheric pressure. Absolute pressure includes both atmospheric pressure and the pressure of the fluid or gas being measured.

2. How is gauge pressure measured?

Gauge pressure is typically measured using a device called a pressure gauge, which contains a pressure-sensitive element such as a diaphragm or a Bourdon tube. The device is calibrated to read zero when there is no pressure applied and then displays the difference between the applied pressure and atmospheric pressure.

3. What units are used to measure gauge pressure?

Gauge pressure is commonly measured in units of pounds per square inch (psi), kilopascals (kPa), or bars (bar). Other units such as inches of water or millimeters of mercury may also be used.

4. How does gauge pressure affect flow velocity?

Gauge pressure plays a significant role in determining the flow velocity of a fluid or gas. In general, a higher gauge pressure will result in a higher flow velocity, while a lower gauge pressure will result in a lower flow velocity. This is because as the pressure increases, the fluid or gas is forced to move faster to maintain the same flow rate.

5. How do changes in temperature affect gauge pressure and flow velocity?

Changes in temperature can affect both the gauge pressure and flow velocity of a fluid or gas. As temperature increases, the volume of the fluid or gas also increases, resulting in a decrease in gauge pressure. This decrease in pressure can also lead to a decrease in flow velocity, as the fluid or gas is less compressed and therefore has less energy to move at the same rate.

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