An ideal fluid flows through a tube at an initial speed of 4.0 m/s. What will be the speed of the fluid if the cross-sectional area of the tube decreases from 6.0 m2 to 2.0 m2?A.1.3 m/sB.4.0 m/sC.12 m/sD.36 m/s
Question
An ideal fluid flows through a tube at an initial speed of 4.0 m/s. What will be the speed of the fluid if the cross-sectional area of the tube decreases from 6.0 m2 to 2.0 m2?A.1.3 m/sB.4.0 m/sC.12 m/sD.36 m/s
Solution
The speed of the fluid can be calculated using the principle of continuity, which states that the mass flow rate must remain constant in a fluid flow. This can be expressed as:
A1V1 = A2V2
where: A1 = initial cross-sectional area V1 = initial speed A2 = final cross-sectional area V2 = final speed
Given: A1 = 6.0 m^2 V1 = 4.0 m/s A2 = 2.0 m^2
We can solve for V2:
V2 = (A1V1) / A2 V2 = (6.0 m^2 * 4.0 m/s) / 2.0 m^2 V2 = 12 m/s
So, the speed of the fluid when the cross-sectional area of the tube decreases from 6.0 m^2 to 2.0 m^2 is 12 m/s. The correct answer is C. 12 m/s.
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