Question
Develop a research plan in order to find out the time it takes the water tank in supplying the school garden.
A rectangular water tank was built with square base 3m long and height 5m. Water tank is initially full of water: water will leak out through the base tap for irrigation at a rate proportional to the total area in contact with water. When the depth of water is 4m, water is filling at the rate of 0.4m/h.
H denotes the depth of water in tank after t, hours.
A. Using Calculus, model this by a differential equation, stating clearly the variables considered. (15marks)
B. Solve the differential equation in [A] giving H in terms of t. Find how long it takes the tank to be half full 2. Find how long the tank irrigates the school garden [10]
C. Give the recommendations on the size of the school garden or side of the water tank or rate of irrigating
A rectangular water tank was built with square base 3m long and height 5m. Water tank is initially full of water: water will leak out through the base tap for irrigation at a rate proportional to the total area in contact with water. When the depth of water is 4m, water is filling at the rate of 0.4m/h.
H denotes the depth of water in tank after t, hours.
A. Using Calculus, model this by a differential equation, stating clearly the variables considered. (15marks)
B. Solve the differential equation in [A] giving H in terms of t. Find how long it takes the tank to be half full 2. Find how long the tank irrigates the school garden [10]
C. Give the recommendations on the size of the school garden or side of the water tank or rate of irrigating
Answers
Anonymous
surely the area of water in contact with the sides cannot affect tha flow rate.
And since the base is rectangular, the area in contact is constant.
Am I missing something here? What is the shape of the base tap, and where is it located?
And since the base is rectangular, the area in contact is constant.
Am I missing something here? What is the shape of the base tap, and where is it located?