A horizontal water pipe goes from a large diameter to a small diameter and then back to the first diameter as shown in the figure below. The level of water (8cm in the larger tube and 4 cm in the constricted tube) in the small vertical tubes provides us with information about the water pressure in the two different sizes of pipe. The inside diameter of the larger pipe is 2.60 cm and water travels through both sizes of pipe with a volume flow rate of 2.00 10-4 m3/s. Determine the inside diameter of the smaller pipe.

Question

A horizontal water pipe goes from a large diameter to a small diameter and then back to the first diameter as shown in the figure below. The level of water (8cm in the larger tube and 4 cm in the constricted tube) in the small vertical tubes provides us with information about the water pressure in the two different sizes of pipe. The inside diameter of the larger pipe is 2.60 cm and water travels through both sizes of pipe with a volume flow rate of 2.00  10-4 m3/s. Determine the inside diameter of the smaller pipe.

I have attempted many times by combining Bernoulli's Equation with the equation of continuity to no avail. Please help.

Bot · Answer

The answer is 1.30 cm. To solve this problem, you need to use the equation of continuity, which states that the flow rate (Q) is equal to the product of the cross-sectional area (A) and the velocity (V) of the fluid. Since the flow rate is given, you can solve for the velocity of the fluid in the two pipes. Then, you can use Bernoulli's equation to calculate the pressure in each pipe. Finally, you can use the pressure difference between the two pipes to calculate the inside diameter of the smaller pipe.