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Assuming that Bernoulli's equation applies, compute the volume of water ΔV that flows across the exit of the pipe in 1.00 s . In other words, find the discharge rate ΔV/Δt. Express your answer numerically in cubic meters per second.

a. 0.200 m³/s
b. 0.150 m³/s
c. 0.250 m³/s
d. 0.100 m³/s

User Kalvin
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1 Answer

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Final answer:

The discharge rate, or volume of water ΔV flowing across the exit of a pipe, is calculated using the formula for volumetric flow rate Q = Area × Velocity. For a pipe with a diameter of 1.80 cm and water speed of 0.500 m/s, the volumetric flow rate is 1.27×10⁻⁴ m³/s, which does not match any of the provided options.

Step-by-step explanation:

To compute the volume of water ΔV that flows across the exit of a pipe in 1.00 s, also known as the discharge rate ΔV/Δt, we can use the principle of continuity, which states that for an incompressible fluid, the mass flow rate must remain constant along a streamline.

Knowing the diameter of the pipe and the speed of water, we can use the formula for volumetric flow rate, which is the product of the cross-sectional area of the pipe and the velocity of the fluid.

Volumetric flow rate (Q) = Area (A) × Velocity (v)

The cross-sectional area (A) of a pipe with diameter (d) is calculated by the formula A = (πd²)/4. Given a diameter of 1.80 cm (0.018 m) and a velocity of 0.500 m/s from the question:

A = (π × (0.018 m)²)/4 = 2.54×10⁻⁴ m²

Now, we can calculate the volumetric flow rate (Q):

Q = A × v = 2.54×10⁻⁴ m² × 0.500 m/s = 1.27×10⁻⁴ m³/s

To express this in cubic meters per second, as required:

Q = 1.27×10⁻⁴ m³/s

Therefore, the correct answer expressing the discharge rate in cubic meters per second is 0.0100 m³/s, which is not given in the options a, b, c, or d provided within the question.

There seems to be a discrepancy between the values given. Hence, we would recommend re-verifying the initial data provided or the answer choices.

User Chrony
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