Question

A horizontal pipe carries a smoothly flowing liquid of density of 1110 kg/m3. At locations 1 and 2 along the pipe, the diameters are 1=6.29 cm and 2=2.39 cm, respectively. What is the ratio of the flow rates at locations 1 and 2?

1) 1:1
2) 1:2
3) 2:1
4) 4:1

Answer 1

The ratio of the flow rates at locations 1 and 2 is approximately 6.914:1.

Step-by-step explanation:

The ratio of the flow rates at locations 1 and 2 can be determined based on the principle of continuity. The principle of continuity states that the volume flow rate of a fluid is constant along a pipe or a duct (assuming incompressible fluid flow).

In this case, the flow rates can be expressed in terms of the cross-sectional areas at locations 1 and 2. The cross-sectional area is proportional to the square of the diameter.

Let's denote the flow rate at location 1 as Q1 and the flow rate at location 2 as Q2. The ratio of the flow rates is given by:

Q1/Q2 = (A1/A2) = (D1^2/D2^2)

Where D1 and D2 are the diameters at locations 1 and 2, respectively.

Plugging in the given diameters, we have:

Q1/Q2 = (6.29^2 cm / 2.39^2 cm) = 39.514 / 5.712 = 6.914

Therefore, the ratio of the flow rates at locations 1 and 2 is approximately 6.914:1.