Question

Water at 20oC flows through a long elliptical duct 30 cm wide and 22 cm high. What average velocity, in m/s, would cause the weight flow to be 500 lbf/s?

Answer 1

Explanation:

The given data is as follows.

   Fluid is water so, density $\rho = 1000 kg/m^{3}$

  Weight flow rate = 500 lbf/s = 2224.11 N/sec

  Cross-sectional area (A) = $\pi \times \frac{30}{2} \times \frac{22}{2}$

                                         = 0.05184 $m^{2}$

Hence, weight flow rate will be given as follows.

        w = $\rho \times g \times A \times V$

    2224.11 N/sec = $\rho \times g \times A \times V$

        V = $\frac{2224.11}{1000 \times 9.81 \times 0.05184}$ m/s

            = 4.373 m/s

Thus, we can conclude that average velocity in the given case is 4.373 m/s.

Answer 2

Answer:

Explanation:

length of major axis, 2a = 30 cm

a = 15 cm = 0.15 m

length of minor axis, 2b = 22 cm

b = 11 cm = 0.11 m

Weight flow, mg = 500 lbf/s = 2224.1 N/s

Area of duct, A = π ab = 3.14 x 0.15 x 0.11 = 0.0518 m²

Let v be the velocity

Volume per second = mass per second / density

Area x velocity = mass per second / density

0.0518 x v = 2224.1 / (9.8 x 1000)

v = 4.4 m/s