# Flow rate in pipe puzzle

1. Jul 16, 2015

### TheNerdyGuy

So we all know that due to the conservation of volume flow rate, reducing the diameter of a hose pipe would increase the velocity of the water flow.(A*V is conserved)
But when the are of an orifice near the bottom of a water tank is reduced the velocity remains the same! Does anyone know why this actually happens?

2. Jul 16, 2015

### Staff: Mentor

In the first part you consider two connected pipes in a single setup, in the second part you compare two completely different setups. There is no reason why those should behave the same.

3. Jul 16, 2015

### TheNerdyGuy

Yes but intuitively when area at a point in the tank is reduced then velocity of the water should increase right?(The water is forced to go through a smaller hole)

4. Jul 16, 2015

### Staff: Mentor

No.
It is forced by the same pressure difference, so it gets the same speed.

What happens without a hole?

5. Jul 16, 2015

### nasu

In the second case the pressure is not changed by reducing the area of the hole. This is the difference.
Your intuition is based on these situations where reduction of area results in increased pressure. Like squeezing a garden hose.

6. Jul 16, 2015

### Staff: Mentor

Far upstream of the hole, the cross sectional area is that of the entire tank, and the velocity is very low. At the oriface, the diameter is much smaller than the tank diameter, and the velocity is much higher. In the region approaching the hole, the streamline pattern is converging, and the effective area for flow is getting smaller as the velocity increases.

Chet

7. Jul 16, 2015

### Khashishi

Flow through a single pipe is conserved, since it's the same water flowing through two parts of the pipe.
Flow through two different tanks doesn't have to be equal between the tanks, since it's not the same water flowing through tank 1 and 2. Obviously, a bigger hole in the bottom of the tank will leak more.