Water flows through a horizontal pipe of varying cross-section at the rate of 10⁻¹ ~m / s . The velocity of water at a point where the radius of the pipe is 10 cm is ( =3 14)

Step-by-step solution

The volume flow rate is defined as Q = Av , where A is the cross-sectional area and v is the velocity. Given the stated rate 10⁻¹ m/s is ambiguous in units; however, in this context the correct interpretation is volume flow rate Q = 10⁻¹ m³/s. For the circular pipe cross-section with radius r = 10 cm = 0.1 m, the area is A = r^2 = (0.1)^2 = 0.01 m². Solving for velocity gives v = Q / A = ( 10⁻¹) / (0.01 ) m/s = 10⁻¹/10⁻² m/s = 10 m/s. Final Answer: C