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alexandr1967 [171]
3 years ago
7

A pipe leads from a storage tank on the roof of a building to the ground floor. The absolute pressure of the water in the storag

e tank where it connects to the pipe is 3.0×105Pa, the pipe has a radius of 1.0 cm where it connects to the storage tank, and the speed of flow in this pipe is 1.6 m/s. The pipe on the ground floor has a radius of 0.50 cm and is 9.0 m below the storage tank. Find the speed of flow in the pipe on the ground floor.
Engineering
1 answer:
Fudgin [204]3 years ago
3 0

Answer:

6.4 m/s

Explanation:

From the equation of continuity

A1V1=A2V2 where A1 and V1 are area and velocity of inlet respectively while A2 and V2 are the area and velocity of outlet respectively

A1=\pi (r1)^{2}

A2=\pi (r2)^{2}

where r1 and r2 are radius of inlet and outlet respectively

v1 is given as 1.6 m/s

Therefore

\pi (0.01)^{2}\times 1.6 = \pi (0.005)^{2}v2

V2=\frac {\pi (0.01)^{2}\times 1.6}{\pi (0.005)^{2}}=6.4 m/s

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The volume of the cylinder v₁= 0.08636 ×(0.09398²)/4 = 5.99×10⁻⁴ m³

The clearance volume = 16% of cylinder volume = 0.16×5.99×10⁻⁴ m³

The clearance volume, v₂  = 9.59 × 10⁻⁵ m³

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T₁ = 60 F = 288.706 K

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\dfrac{T_{3}}{T_{4}} = \left (\dfrac{v_{4}}{v_{3}}  \right )^{K-1}

T₄ = 2888.89 / 6.25^{0.393} = 1406.5 K

Work done, W = c_v×(T₃ - T₂) - c_v×(T₄ - T₁)

0.718×(2888.89  - 592.984) - 0.718×(1406.5 - 288.706) = 845.88 kJ/kg

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