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(a) (b) Apply the energy balance between the free surface of the tank liquid and the discharge and show that the discharge velocity is Ит pgr² (h+L) 8μL Use the mass balance to show that the height of the liquid h is governed by dh pgr¹ (h+L) dt 8R²μL Integrate the above equation and show that the time taken to drain the tank (c) completely is: 8μLR² t= In 1+ pgr4 (1+77) H h R H 2r L ?

(a) (b) Apply the energy balance between the free surface of the tank liquid and the discharge and show that the discharge velocity is Ит pgr² (h+L) 8μL Use the mass balance to show that the height of the liquid h is governed by dh pgr¹ (h+L) dt 8R²μL Integrate the above equation and show that the time taken to drain the tank (c) completely is: 8μLR² t= In 1+ pgr4 (1+77) H h R H 2r L ?

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
Problem 1.1MA
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The tank and pipe shown in the following figure are initially filled with a liquid of
viscosity μ and density ρ. You can assume laminar flow and ignore exit kinetic-energy
effects. Friction is important in the tube descending from the bottom of the tank, but you can
assume negligible friction in the large tank.
(a)  Apply the energy balance between the free surface of the tank liquid and the
discharge and show that the discharge velocity is the equation seen in the image
(b)  Use the mass balance to show that the height of the liquid h is governed by the equation in the image
(c)  Integrate the equation shown in the image and show that the time taken to drain the tank
completely is: 

(a) (b) Apply the energy balance between the free surface of the tank liquid and the discharge and show that the discharge velocity is Ит pgr² (h+L) 8μL Use the mass balance to show that the height of the liquid h is governed by dh pgr¹ (h+L) dt 8R²μL Integrate the above equation and show that the time taken to drain the tank (c) completely is: 8μLR² t= In 1+ pgr4 (1+77) H h R H 2r L ?
Transcribed Image Text:(a) (b) Apply the energy balance between the free surface of the tank liquid and the discharge and show that the discharge velocity is Ит pgr² (h+L) 8μL Use the mass balance to show that the height of the liquid h is governed by dh pgr¹ (h+L) dt 8R²μL Integrate the above equation and show that the time taken to drain the tank (c) completely is: 8μLR² t= In 1+ pgr4 (1+77) H h R H 2r L ?
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