Question

One end of a cylinderical pipe has a radius 1.5cm and water streams steadily out at 7m/s . The volume flow rate is..... ?

Answer 1

Kindly refer attachment for solution

Answer 2

We know that, Volume of an Object is the Amount of Space occupied by the Object which is given by Multiplying the Area of Space occupied by the Object and the Height of the Object.

✿  Volume = Area × Height (or Length)

In the Similar way, Volume Flow Rate is Defined as the Amount of Liquid which is Passing from a Point in One Second. The Words ''Flow Rate" indicate the Liquid flowing per second.

Now, In order to Calculate the Volume Flow Rate, First we need to Calculate the Area of the Pipe through which the Liquid is Flowing.

Given : The Radius of Cylindrical Pipe is 0.015m

We know that Cross Section of Cylindrical Pipe is Circular in Shape

⇒ Area of Circular Shape of the Cylindrical Pipe is given by : πr²

⇒ Area of Circular Shape of the Cylindrical Pipe is $\bf{: [\frac{22}{7} \times (0.015)^2]}$

⇒ Area of Circular Shape of the Cylindrical Pipe is 7 × 10⁻⁴ m²

Given : Water streams steadily at 7 m/sec

⇒ The Volume Flow Rate = (7 × 7 × 10⁻⁴) m³/sec

⇒ The Volume Flow Rate = 49 × 10⁻⁴ m³/sec

We know that : One m³ = 1000 Liter

⇒ The Volume Flow Rate = 49 × 10⁻⁴ × 1000 Liter/sec

⇒ The Volume Flow Rate = 4.9 Liter/sec

In General : Volume Flow rate is given by :

✿  Q = V × A

where :

$\heartsuit$ V is the Flow Velocity

$\heartsuit$ A is the Cross sectional Area through which the Fluid flows.

Note : The Diagram is made using a Bad Scale.