As shown in the diagram, brine of specific gravity draining from the bottom of the large tank through a 100 mm pipe, the drain pipe ends at a point 20m below the surface of the brine in the tank. Calculate the velocity of flow along the streamline at the point of discharge from the pipe. a.20 m/sb.14 m/sc.19 m/sd.19.8 m/s
Question
As shown in the diagram, brine of specific gravity draining from the bottom of the large tank through a 100 mm pipe, the drain pipe ends at a point 20m below the surface of the brine in the tank. Calculate the velocity of flow along the streamline at the point of discharge from the pipe. a.20 m/sb.14 m/sc.19 m/sd.19.8 m/s
Solution
To solve this problem, we can use Torricelli's theorem, which states that the speed v of efflux of a fluid under the force of gravity from a hole in a large, open tank is given by v = sqrt(2gh), where g is the acceleration due to gravity and h is the height of the fluid above the hole.
Given:
- g = 9.81 m/s^2 (acceleration due to gravity)
- h = 20 m (height of the fluid above the hole)
Substitute these values into the equation:
v = sqrt(2 * 9.81 m/s^2 * 20 m) = sqrt(392.4 m^2/s^2) = 19.8 m/s
So, the velocity of flow along the streamline at the point of discharge from the pipe is approximately 19.8 m/s. Therefore, the correct answer is d.19.8 m/s.
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