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When water leaks through a hole, friction and contraction of the stream near the hole reduce the volume of water leaving the tank per second to CA,V 2gh, where c (0 0. The radius of the hole is 4 in., g = 32 ft/s?, and the friction/contraction factor is c = 0.6. (Assume the removed apex of the cone is of negligible height and volume.) 125 dh ft/s dt 24h

When water leaks through a hole, friction and contraction of the stream near the hole reduce the volume of water leaving the tank per second to CA,V 2gh, where c (0 0. The radius of the hole is 4 in., g = 32 ft/s?, and the friction/contraction factor is c = 0.6. (Assume the removed apex of the cone is of negligible height and volume.) 125 dh ft/s dt 24h

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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When water leaks through a hole, friction and contraction of the stream near the hole reduce the volume of water leaving the tank per second to CA,V 2gh, where c (0 <c< 1) is an empirical constant. Find an equation for the volume V (in ft/s3) of water in the tank in terms of the height of the water h. 4 V = 757 ft/s3 Find the rate of change of the height of the water in terms of the height of the water h and the rate of change of the volume of the water. 25 dh dv 4nh dt dt Determine a differential equation for the height of the water h (in ft/s in terms of h) at time t > 0. The radius of the hole is 4 in., g = 32 ft/s?, and the friction/contraction factor is c = 0.6. (Assume the removed apex of the cone is of negligible height and volume.) 125 dh ft/s dt 24h
Transcribed Image Text:When water leaks through a hole, friction and contraction of the stream near the hole reduce the volume of water leaving the tank per second to CA,V 2gh, where c (0 <c< 1) is an empirical constant. Find an equation for the volume V (in ft/s3) of water in the tank in terms of the height of the water h. 4 V = 757 ft/s3 Find the rate of change of the height of the water in terms of the height of the water h and the rate of change of the volume of the water. 25 dh dv 4nh dt dt Determine a differential equation for the height of the water h (in ft/s in terms of h) at time t > 0. The radius of the hole is 4 in., g = 32 ft/s?, and the friction/contraction factor is c = 0.6. (Assume the removed apex of the cone is of negligible height and volume.) 125 dh ft/s dt 24h
8 ft 20 ft h `circular hole When water leaks through a hole, friction and contraction of the stream near the hole reduce the volume of water leaving the tank per second to cA,V 2gh, where c (0 <c< 1) is an empirical constant. Find an equation for the volume V (in ft/s) of water in the tank in terms of the height of the water h. 4 V = 75 ft/s3 Find the rate of change of the height of the water in terms of the height of the water h and the rate of change of the volume of the water. dh 25 dV dt 4th dt
Transcribed Image Text:8 ft 20 ft h `circular hole When water leaks through a hole, friction and contraction of the stream near the hole reduce the volume of water leaving the tank per second to cA,V 2gh, where c (0 <c< 1) is an empirical constant. Find an equation for the volume V (in ft/s) of water in the tank in terms of the height of the water h. 4 V = 75 ft/s3 Find the rate of change of the height of the water in terms of the height of the water h and the rate of change of the volume of the water. dh 25 dV dt 4th dt
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