An ideal fluid,of density 0.90 ´ 10³ kg/m³,flows at 6.0 m/s through a level pipe with radius of 0.50 cm.The pressure in the fluid is 1.3 ´ 10⁵ N/m².This pipe connects to a second level pipe,with radius of 1.5 cm.Find the speed of flow in the second pipe. A)54 m/s B)18 m/s C)0.67 m/s D)0.33 m/s

Question

Quizplus · Accepted Answer

We can use the principle of continuity for ideal fluids which states that the product of the cross-sectional area and the speed of flow is constant throughout the fluid. 
Thus, A1v1 = A2v2 where A1 and A2 are the cross-sectional areas of pipes 1 and 2 respectively, and v1 and v2 are the speeds of flow.
Using this equation and the formula for the cross-sectional area of a pipe (A = πr^2), we can find v2: 
A1 = π(0.005m)^2 = 7.85 ´ 10^-5 m^2 
A2 = π(0.015m)^2 = 7.07 ´ 10^-4 m^2 
v1 = 6.0 m/s

Solving for v2, we get:
v2 = (A1v1)/A2 = (7.85 ´ 10^-5 m^2 × 6.0 m/s)/(7.07 ´ 10^-4 m^2) ≈ 0.67 m/s

Therefore, the best choice is C.

An Ideal Fluid,of Density 0