Help! Calculating Water Flow Rate in Pipe

[Sevy35]

Please help I'm going round in circles!

Water on tank 12m high, feeding pipe 200m long and 125mm diameter. Open end.

Given friction factor of 0.008 for the pipe and total of 3.2K for various fittings.

Asked to find water flow rate in Kg/s in the pipe.

Been looking at this for ages now and have got really confused!

So far :

As the tank and the outlet are open to the atmosphere we can use v= √2gh to find the velocity of the water?

V=√(2*9.81*12)

V=15.34m/s

Mass flow rate =pVA
Where p is the density of water 1000kg/m3
V is mean velocity 15.34m/s
A is cross sectional area normal to the direction of flow 0.125mXπ2
2
m = 1000 x 15.34 x (0.125xπ2)
2

 

[tiny-tim]

Hi Sevy35!

… Been looking at this for ages now and have got really confused!

Yes … since last December, I see! … https://www.physicsforums.com/showthread.php?t=278890

So far :

As the tank and the outlet are open to the atmosphere we can use v= √2gh to find the velocity of the water?

No, you can use ρgh, but only to find the contribution of the height to the Bernoulli's equation.

As LowlyPion said, you must subtract the loss through friction.

Remember the background: Bernoulli's equation is basically a conservation of energy equation (per unit mass, ie using density instead of mass), and if you have friction, you must subtract the energy lost from friction (equals the work done by friction).

 

[tomcue]

m= 7.55kg/s


Hello there! It seems like you're having trouble calculating the water flow rate in your pipe. Don't worry, I can help you with that. Let's break down the steps to make it easier for you.

First, you're on the right track by using the formula v=√2gh to find the velocity of the water. This formula is known as the Bernoulli's equation, which relates the pressure, velocity, and height of a fluid in a pipe. In your case, the water in your tank has a height of 12m, so the velocity will be √(2*9.81*12) = 15.34m/s.

Next, you can use the formula for mass flow rate: m = pVA, where p is the density of water (1000kg/m3), V is the mean velocity (15.34m/s), and A is the cross sectional area normal to the direction of flow (0.125m x π/4 = 0.098m2). This will give you a mass flow rate of 1000 x 15.34 x 0.098 = 15.03kg/s.

However, you also need to take into account the friction factor and total head loss due to fittings in the pipe. To do this, you can use the Darcy-Weisbach equation: hL = f(L/D)(V2/2g), where hL is the head loss, f is the friction factor (0.008), L is the length of the pipe (200m), D is the diameter of the pipe (125mm = 0.125m), V is the velocity (15.34m/s), and g is the acceleration due to gravity (9.81m/s2). This will give you a total head loss of 3.36m.

Now, to find the actual velocity of the water in the pipe, you can use the modified Bernoulli's equation: V = √2gh - √2ghL, where h is the height of the water in the tank (12m) and hL is the head loss (3.36m). This will give you a velocity of 15.28m/s.

Finally, you can use the mass flow rate formula again, but this time with the actual velocity (15.28m/s) to