Final answer:
The flow rate of water in a horizontal pipe can be determined using the equation of continuity. By applying this equation to the given scenario, we can find the velocity of the water when the pipe narrows down to 1.50 cm.
Step-by-step explanation:
The speed of water flowing through a horizontal pipe can be calculated using the equation of continuity, which states that the product of the cross-sectional area and the velocity of the fluid is constant. Hence, A₁V₁ = A₂V₂, where A₁ and A₂ are the cross-sectional areas at two different points, and V₁ and V₂ are the velocities at those points.
In this case, the initial diameter of the pipe is 2.20 cm, and the final diameter is 1.50 cm. The flow rate, which is the product of the cross-sectional area and the velocity, remains constant. Therefore, we can use the equation A₁V₁ = A₂V₂ to find the velocity of the water when the pipe narrows down to 1.50 cm.
Let's denote the initial velocity as V₁ and the final velocity as V₂. The initial diameter is 2.20 cm, which means the initial radius is 1.10 cm. The final diameter is 1.50 cm, which means the final radius is 0.75 cm. We can write the equation as π(1.10 cm)²(V₁) = π(0.75 cm)²(V₂). Simplifying this equation, we get (1.10 cm)²(V₁) = (0.75 cm)²(V₂). Dividing both sides of the equation by (0.75 cm)² gives us (V₁) = ((0.75 cm / 1.10 cm)²)(V₂).
Therefore, the correct option is B) (1.50/2.20)×3.50 m/s. By substituting the given values in this equation, we can find the velocity of the water when the pipe narrows down to 1.50 cm.