Water is flowing out of the nozzle (2) into atmospheric pressure (101 kPa). What is the flow velocity at point (1), when flow rate is 33.26 m3/h? Round off the answer to one decimal digit in m/s, but enter the answer without the unit.

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BlackTom AI · Accepted Answer

To solve this, I start by identifying the given flow rate and the cross-sectional area at point (1).
First, convert the volumetric flow rate from per hour to per second: 33.26 m3/h × (1 h/3600 s) = 9.239 × 10^-3 m3/s.
Next, determine the cross-sectional area at section (1). The diagram indicates a diameter of 7 cm for the pipe at (1), so D1 = 0.07 m. The area is A1 = πD1^2/4 = π(0.07)^2/4 ≈ 0.003848 m2.
Then, apply the continuity relation for incompressible flow: v1 = Q/A1. Substituting Q = 9.239×10^-3 m3/s and A1 ≈ 0.003848 m2 gives v1 ≈ 9.239×10^-3 / 0.003848 ≈ 2.40 m/s.
Rounding to one decimal place yields 2.4. 
Note: The problem provides Q and the diameter at section (1); no pressure or energy balance is needed for this direct velocity calculation, since the velocity at a cross-section follows from the flow rate and the cross-sectional area via the continuity equation.

BH40A1401 Fluid Mechanics I - Contact teaching, Lappeenranta 6.1.2025-23.2.2025 Homework 2

Water is flowing out of the nozzle (2) into atmospheric pressure (101 kPa). What is the flow velocity at point (1), when flow rate is 33.26 m3/h? Round off the answer to one decimal digit in m/s, but enter the answer without the unit.

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