Explanation Given information: The diameter of the reentrant orifice is D . The position of the orifice below the surface of the tank is h . The speed of the stream as v = 2 g h . The speed of approach as v 1 = 0 . Calculation: From hydrostatics condition, The pressure at section 1 is as follows: p 1 = γ h = ρ g h The pressure at section 2 is p 2 = 0 Calculate the area of the orifice ( A 1 ) as shown below. A 1 = π D 2 4 Calculate the area of the stream ( A 2 ) as shown below. A 2 = π d 2 4 Sketch the stream of the orifice as shown in Figure 1. Refer to Figure 1. Calculate the length of the slipstream ( Δ l ) as shown below. Δ l = v Δ t . Here, v is the velocity of the air and Δ t is the time. Calculate the mass rate of flow ( d m d t ) as shown below. mass = density × volume = density × area × length Δ m = ρ A 2 Δ l Substitute v Δ t for Δ l . Δ m = ρ A 2 v Δ t Δ m Δ t = ρ A 2 v d m d t = ρ A 2 v Sketch the Free Body Diagram of the orifice as shown in Figure 2. Refer to Figure 2. Calculate the diameter of the stream ( d ) as shown below. Apply the principle of impulse and momentum as shown below

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Author: BEER

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The study of the flow of gases and liquids, usually in and around solid surfaces, is known as fluid dynamics in physics and engineering. Fluid dynamics, for example, can be used to evaluate the movement of air through an airplane wing or the surface of a…

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Chapter 14.3, Problem 14.82P

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Show that the diameter of the stream is d=D2.

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Chapter 14.3, Problem 14.81P

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Show that the diameter of the stream is d = D 2 .

Solution Summary: The author shows that the diameter of the stream is d=Dsqrt2 and the speed of approach as v_1=0.

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