(a) By applying Bernoullis equation and theĮquation of continuity to points 1 and 2, show that v = ρ ( a 2 − A 2 ) 2 a 2 △ p , (Here △ p means pressure in the throat minus pressure in the pipe.) The change in the fluids speed is accompanied by a change △ p in the fluids pressure, which causes a height difference h of the liquid in the two arms of Portion of the meter to the narrower portion. Pipe with speed V and then through a narrow throat of cross-sectional area a with speed v. Between the entrance and exit, the fluid flows from the The meter is connected between two sections of the pipe the cross-sectional area A of the entrance and exit of the meter matches the pipes cross-sectional area. This phenomenon isĪ venturi meter is used to measure the flow speed of a fluid in a pipe. Object falling freely through a vertical distance h. Hole a distance h below the surface is equal to that acquired by an In other words, for an open tank, the speed of liquid coming out through a V 1 = ρ 2 p (so that the term 2 g h can be neglected), P = P o v 1 = 2 g h Applying Bernoulli's equation to points 1 and 2 and noting that at the hole P 1 is equal to atmospheric pressure P 0 , we find that P 0 + 2 1 ρ v 1 2 + ρ g y 1 = P + ρ g y 2 Determine the speed of the liquid as it leaves the hole when the liquid's level is a distance h above the hole.Ī 2 > A 1 , the liquid is approximately at rest at the top of the tank, where the pressure is P. The air above the liquid is maintained at a pressure P. Torricelli's law is a theorem in fluid dynamics relating the speed of fluid flowing out of an opening to the height of fluid above the opening.Īn enclosed tank containing a liquid of density ρ has a hole in its side at a distance y 1 from the tank's bottom (Fig.) The hole is open to the atmosphere, and its diameter is much smaller than the diameter of the tank.
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