A cylinder has a diameter of 15cm. The water level in the cylinder is maintained at a constant height of .45m. If the diameter of the spout pipe is .50cm how high is the vertical stream of water?Assume water to be an ideal fluid
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To find the height of the vertical stream of water, we can use the principles of fluid mechanics. Here's how you can calculate it:
1. Convert the diameter of the cylinder from cm to meters:
Diameter = 15 cm = 0.15 m
2. Calculate the cross-sectional area of the cylinder:
Radius = Diameter / 2 = 0.15 m / 2 = 0.075 m
Cross-sectional area = π * (Radius^2) = π * (0.075 m)^2 = 0.0177 m^2
3. Determine the volume of water flowing through the spout per second:
Since the water level is maintained at a constant height, the volume of water flowing out per second will be equal to the volume of the cross-section of the cylinder.
Volume flow rate = Cross-sectional area * Speed of water flow
In this case, since we are assuming the water to be an ideal fluid, the speed of water flow is constant.
Volume flow rate = 0.0177 m^2 * Speed of water flow (m/s)
4. Calculate the speed of water flow at the spout:
Since the diameter of the spout pipe is given, we can calculate its radius:
Radius of spout pipe = Diameter / 2 = 0.50 cm / 200 cm/m = 0.005 m
Assuming the flow through the pipe to be fully developed, the speed of water at the spout can be calculated using the principle of conservation of mass:
Cross-sectional area of spout pipe * Speed of water flow = Cross-sectional area of cylinder * Speed of water flow at the top
Speed of water flow at the spout = (Cross-sectional area of cylinder * Speed of water flow at the top) / Cross-sectional area of spout pipe
5. Now that we have calculated the speed of water flow at the spout, we can calculate the height of the vertical stream of water:
Height of vertical stream = Speed of water flow at the spout * Time taken
Please provide the value of the speed of water flow or the time taken so that we can compute the height of the vertical stream of water accurately.