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(c) As shown in Figure 2.4(a), a liquid of constant density p drains from a large tank to the surrounding atmosphere through a long circular pipe of length h and diameter D. Exasperated that it is taking so long to drain the tank, a simple-minded engineer removes the tube so that the liquid drains directly to the surrounding atmosphere through a hole of diameter D, as shown in Figure 2.4(b). The engineer also tries to replace the constant diameter pipe with a tapered pipe having inlet and outlet diameters of D and 0.5D, respectively, and a length of h, as shown in Figure 2.4(c). The tapered pipe's diameter varies linearly along the length of the pipe. In all three cases, the height of the liquid in the tank is H and it is assumed that the liquid level in the tank falls very slowly. Assume that the flow is inviscid, and that the pipes are completely filled with liquid. The liquid's exit velocities are V₁, V2 and V3 for Figures 2.4(a), (b) and (c), respectively. (i) Express V₁, V2 and V3 in terms of the given quantities. (ii) For Figure 2.4(c), obtain an expression (in terms of the given quantities) for the gage pressure at a general point M which is located at an elevation z above the tapered pipe's outlet. Assume that the flow through the tapered pipe is one-dimensional and is only a function of z. ↓v₁ (a) TI➜ af -Pipe of constant diameter D Q P 0.5D V₂ V3 -Pipe of constant diameter D (b) -Tapered Pipe (b) -Hole of diameter D

(c) As shown in Figure 2.4(a), a liquid of constant density p drains from a large tank to the surrounding atmosphere through a long circular pipe of length h and diameter D. Exasperated that it is taking so long to drain the tank, a simple-minded engineer removes the tube so that the liquid drains directly to the surrounding atmosphere through a hole of diameter D, as shown in Figure 2.4(b). The engineer also tries to replace the constant diameter pipe with a tapered pipe having inlet and outlet diameters of D and 0.5D, respectively, and a length of h, as shown in Figure 2.4(c). The tapered pipe's diameter varies linearly along the length of the pipe. In all three cases, the height of the liquid in the tank is H and it is assumed that the liquid level in the tank falls very slowly. Assume that the flow is inviscid, and that the pipes are completely filled with liquid. The liquid's exit velocities are V₁, V2 and V3 for Figures 2.4(a), (b) and (c), respectively. (i) Express V₁, V2 and V3 in terms of the given quantities. (ii) For Figure 2.4(c), obtain an expression (in terms of the given quantities) for the gage pressure at a general point M which is located at an elevation z above the tapered pipe's outlet. Assume that the flow through the tapered pipe is one-dimensional and is only a function of z. ↓v₁ (a) TI➜ af -Pipe of constant diameter D Q P 0.5D V₂ V3 -Pipe of constant diameter D (b) -Tapered Pipe (b) -Hole of diameter D

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
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(c) As shown in Figure 2.4(a), a liquid of constant density p drains from a large tank to the surrounding atmosphere through a long circular pipe of length h and diameter D. Exasperated that it is taking so long to drain the tank, a simple-minded engineer removes the tube so that the liquid drains directly to the surrounding atmosphere through a hole of diameter D, as shown in Figure 2.4(b). The engineer also tries to replace the constant diameter pipe with a tapered pipe having inlet and outlet diameters of D and 0.5D, respectively, and a length of h, as shown in Figure 2.4(c). The tapered pipe's diameter varies linearly along the length of the pipe. In all three cases, the height of the liquid in the tank is H and it is assumed that the liquid level in the tank falls very slowly. Assume that the flow is inviscid, and that the pipes are completely filled with liquid. The liquid's exit velocities are V₁, V2 and V3 for Figures 2.4(a), (b) and (c), respectively. (i) Express V₁, V₂ and V3 in terms of the given quantities. (ii) For Figure 2.4(c), obtain an expression (in terms of the given quantities) for the gage pressure at a general point M which is located at an elevation z above the tapered pipe's outlet. Assume that the flow through the tapered pipe is one-dimensional and is only a function of z. P V₁ (a) H !! -Pipe of constant diameter D P 0.5D P D V/₂✓ V3 Pipe of constant diameter D (b) -Tapered Pipe (b) -Hole of diameter D
Transcribed Image Text:(c) As shown in Figure 2.4(a), a liquid of constant density p drains from a large tank to the surrounding atmosphere through a long circular pipe of length h and diameter D. Exasperated that it is taking so long to drain the tank, a simple-minded engineer removes the tube so that the liquid drains directly to the surrounding atmosphere through a hole of diameter D, as shown in Figure 2.4(b). The engineer also tries to replace the constant diameter pipe with a tapered pipe having inlet and outlet diameters of D and 0.5D, respectively, and a length of h, as shown in Figure 2.4(c). The tapered pipe's diameter varies linearly along the length of the pipe. In all three cases, the height of the liquid in the tank is H and it is assumed that the liquid level in the tank falls very slowly. Assume that the flow is inviscid, and that the pipes are completely filled with liquid. The liquid's exit velocities are V₁, V2 and V3 for Figures 2.4(a), (b) and (c), respectively. (i) Express V₁, V₂ and V3 in terms of the given quantities. (ii) For Figure 2.4(c), obtain an expression (in terms of the given quantities) for the gage pressure at a general point M which is located at an elevation z above the tapered pipe's outlet. Assume that the flow through the tapered pipe is one-dimensional and is only a function of z. P V₁ (a) H !! -Pipe of constant diameter D P 0.5D P D V/₂✓ V3 Pipe of constant diameter D (b) -Tapered Pipe (b) -Hole of diameter D
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