Cub bernoulli lesson01_bernoulliflowgraphics_v3_sas
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Bernoulli's principle states that as water flows through a pipe from a high elevation reservoir to a lower elevation, its velocity increases to maintain the total energy of the water. Applying the Bernoulli equation between two points in the streamline allows calculating unknown parameters like velocity. In this example, the equation is simplified by eliminating terms that drop out, and used to calculate the velocity of water flowing from a 250m high reservoir, found to be 70 m/s.
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Cub bernoulli lesson01_bernoulliflowgraphics_v3_sas
- 2. v1 v2 Ground (h = 0) h1 h2 P1 P2 As the water loses elevation from the high end of the pipe to the low end, it gains velocity. To find the exact value of any parameter, we apply the Bernoulli equation to two points anywhere along the same streamline. streamline
- 3. h1 = 250 m P1 = atmospheric h2 = 0 m P2 = atmospheric The water at the top of the reservoir starts at rest, so v1 is zero, and the first term drops out. Since the final height (h2) is also zero, this term drops out, too. Lastly, P1 = P2, which is atmospheric pressure, so these terms drop out as well. Plugging in the remaining the known parameters: ρwater g (250 m) = ½ ρwater v2 2 Now the ρwater terms can be cancelled out. Using g = 9.8 m/s2 and solving for v2, we have v2 = sqrt (2*9.8 m/s2 * 250 m) v2 = 70 m/s