Water Exercises: River Flow and Boat Speed

1. Water exercises

2. 1.Johnny is a passionate swimmer. He built a swimming pool of 20 metres length , 3 metres width , 2 metres depth at his grandparents’ yard because through his grandparents’ yard a river crossed ,Johnny managed to build a water –stop/lock with which he could reverse the course of the river to his own pool this way he noticed that he could fill his pool in 40 minutes. • TASK: Calculate the debit of the river in the moment he filled his pool.

3. Solution: Pool dimensions : L-20 w-3 d-2 Volume of the pool L*w*d=20*3*2=120cubic m 1m3=1000 liters Volume of the pool=120000 liters Debit =volume/time=120000(40*50)=50l/s

4. 2.Johnny has a motor boat because he likes water a lot and takes rides on the river. He often goes to see his friend Gill who lives 6 km upstream. Johnny noted that going there takes 20 minutes and coming back it takes 40 minutes. • Task: Help Johnny to calculate the velocity of the river flow and also calculate the speed that the boat can reach if it was driven on a lake.

5. Solution: If we write: V=the velocity of the river U=the velocity of the boat separate from water V1=velocity upstream V2=velocity downriver Then, u+v=the velocity of the boat from the bank in the same current with water u-v=the velocity of the boat contrary to the flow • v1 velocity downstream is distance/time=6000(20*60)=5 m/s • v2 velocity upstream is distance/time=6000(40*60)=2.5 m/s • 2u=7,5m/s u = 3,75 m/s • v= v1 – u v= 5 – 3,75 v= 1,25 m/s • the velocity of the boat is 3.75m/s=13.5hm/h • the velocity of water is 1,25 m/s = 4,5 km/h