A siphoning tool is used while cleaning an aquarium to remov

A siphoning tool is used while cleaning an aquarium to remove water from the tank. Assuming the Bernoulli equation is valid, what can you do to decrease the amount of time it takes to empty the aquarium?

Solution

Lets us assume we havesiphoning tool which is type of  centrifugal pump with a service of water and designed discharge pressure of 10 kg/cm2 and we are using this pump for sending water Out of tank which is 1000 m away from pump.

Now, as the pump is centrifugal, it will generate constant head (discharge pressure), but we can vary its flow rate.

Case:
Suppose pump discharge valve is 30% open, output values: discharge pressure=10 kg/cm2 and assume mass flow rate at 30% opening = 50 kg/hr.

Now, at the just outlet of pump P = 10 kg/cm2.
at distance of 500 m, P = 10 - dP
where as dp = {8 * viscosity * length (500 in this case) * mass flow rate (50 in this case)} / {3.14 * (radius of pipe)^4 * density }........by hagen poise eq.

MEANS, dP is directly proportion to (length) * (mass flow rate)

P will decrease along the length of pipe keeping mass flow rate constant.

We can vary the mass flow rate by changing discharge valve opening. Discharge pressure will remain same in case of centrifugal pump. Thus, we can measure Pressure P at any point on the pipe by measuring dP across certain length of pipe.

That means by changing the Area of Flow We can change Flow rate and Time will change as per that .

Lower the area of flow, Presure will be high , which will consume less time ,

this way ,decrease the amount of time it takes to empty the aquarium