Question

a farmer connects A pipe of internal diameter 25 cm from a Canal into a cylindrical tank in his field which is 12 m in diameter and 2.5 M deep if water flows through the pipe at the rate of 3.6 km per hour in how much time will the tank be filled also find the cost of water is the canal department charges @ rupees 0.07 per metre cube

Answer 1

Step-by-step explanation:

1. 25/2cm is when converted into metre gives 1/8m
2. pi is taken as 22/7
3. 3.6km/hr is when converted into metre per second gives 3600.

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Answer 2

given the speed of water through pipe outlet for a water tank, find the time taken to fill the tank and cost of water

Explanation:

1. given the diameter of water tank $d=12\ m$  and depth of the tank $D=2.5\ m$, then the volume of the cylindrical water tank is given by,                  $V=\frac{\pi d^2D}{4}\\V=\frac{\pi (12)^2(2.5)}{4}\\ V=90\pi \ m^3$      
2. now the speed of water flowing in pipe is, $s=3.6\ km/hr= 1\ m/s$
3. now given the radius of the pipe $r=25cm$ the volume flow rate is given by,   $v=\pi r^2s=\pi (0.25)^{2}(1) \ \ \ \ \ \ \ \ ->v= 0.0625\pi \ m^3/s$        
4. now the time taken to fill the tank is ,                                                             $t=\frac{V}{v} \\\\t=\frac {90\pi }{0.0625\pi } \\\\t=1440\ s$                  ------->ANSWER
5. now the cost of water decided by canal department is $p=Rs.0.07/m^3$          then, the total cost of water is ,                                      $T=pV=0.07(90\pi )\\\\T=0.07(90)(\frac{22}{7} )\\\\T=Rs.19.8$                 ---------->ANSWER