For the Flow Tab:(In this simulation, the flow rate out of the pipe at the left end is kept at a constant value shown in the box in the upper left corner.) 1. With the friction box unchecked, check the box for flux meter to place a flux meter in the middle of the pipe. Move the speed gauge to different locations inside the pipe to take speed reading. What do you find from the speed gauge? Now use a handle in the middle to make the pipe narrower in the middle. Record the readings of the flux meter: Flow rate: , area: - (flux: Ignore this reading and the way "flux "is used in this simulation because the term"flux"can be ambiguous.). Which of these quantities stayed the same when you change the size of the pipe and why?Please also move the speed gauge around to see how the speed varies at different locations inside the pipe. 3. What do you think will happen qualitatively to these 2 readings of the flux meter if you use a handle in the middle to make the pipe wider in the middle? Flow rate: Do the actual reading match your expectations? , area: se around to see how the speed varies Please also move the speed gauge at different locations inside the pipe. Briefly write down your observations.

Question

For the Flow Tab:(In this simulation, the flow rate out of the pipe at the left end is kept at a constant value shown in the box in the upper left corner.) 1. With the friction box unchecked, check the box for flux meter to place a flux meter in the middle of the pipe. Move the speed gauge to different locations inside the pipe to take speed reading. What do you find from the speed gauge? Now use a handle in the middle to make the pipe narrower in the middle. Record the readings of the flux meter: Flow rate: , area: - (flux: Ignore this reading and the way "flux "is used in this simulation because the term"flux"can be ambiguous.). Which of these quantities stayed the same when you change the size of the pipe and why?Please also move the speed gauge around to see how the speed varies at different locations inside the pipe. 3. What do you think will happen qualitatively to these 2 readings of the flux meter if you use a handle in the middle to make the pipe wider in the middle? Flow rate: Do the actual reading match your expectations? , area: se around to see how the speed varies Please also move the speed gauge at different locations inside the pipe. Briefly write down your observations.

Answer 1

1. **Speed Gauge Observations:** - When you move the speed gauge to different locations inside the pipe, you will likely observe that the speed of the fluid is uniform throughout the pipe when there are no changes in the pipe's diameter and friction is not considered. This is because the flow rate is constant, and the cross-sectional area of the pipe remains the same.2. **Narrowing the Pipe:** - **Flow Rate:** The flow rate should remain constant even when the pipe is narrowed. This is due to the principle of conservation of mass, which states that for an incompressible fluid, the mass flow rate must remain constant throughout the pipe. - **Area:** The area of the pipe decreases where it is narrowed. - **Speed Variation:** As the pipe narrows, the speed of the fluid increases at the narrower section. This is consistent with the principle of continuity, which states that

, where

is the cross-sectional area and

is the velocity. Therefore, a decrease in area results in an increase in velocity to maintain a constant flow rate.3. **Widening the Pipe:** - **Qualitative Expectations:** - **Flow Rate:** The flow rate should remain constant. - **Area:** The area of the pipe increases where it is widened. - **Actual Observations:** - If you widen the pipe, the speed of the fluid decreases in the wider section. This is again explained by the continuity equation, where an increase in area leads to a decrease in velocity to keep the flow rate constant. - **Speed Variation:** By moving the speed gauge around, you should observe that the speed is lower in the wider section compared to the rest of the pipe.These observations align with the principles of fluid dynamics, specifically the continuity equation, which governs the relationship between flow rate, velocity, and cross-sectional area in a pipe.

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