Question

g 1. Water flows through a 30.0 cm diameter water pipe at a speed of 3.00 m/s. All of the water in the pipe flows into a smaller pipe that is 10.0 cm in diameter. Determine: a) The speed of the water flowing through the 10.0 cm diameter pipe. b) The mass of water that flows through the larger pipe in 1.00 minute. c) The mass of water that flows through the smaller pipe in 1.00 minute.

Answer 1

a) v₂ = 30 m/s

b) m₁ = 12600 kg

c) m₂ = 12600 kg

Step-by-step explanation:

a)

Using the continuity equation:

`A_1v_1 = A_2v_2`

where,

A₁ = Area of inlet = π(0.15 m)² = 0.07 m²

A₂ = Area of outlet = π(0.05 m)² = 0.007 m²

v₁ = speed at inlet = 3 m/s

v₂ = speed at outlet = ?

Therefore,

`(0.07\ m^2)(3\ m/s)=(0.007\ m^2)v_2\\\\v_2 = (0.21\ m^3/s)/(0.007\ m^2)`

v₂ = 30 m/s

b)

`m_1 = \rho A_1v_1t`

where,

m₁ = mass of water flowing in = ?

ρ = density of water = 1000 kg/m³

t = time = 1 min = 60 s

Therefore,

`m_1 = (1000\ kg/m^3)(0.07\ m^2)(3\ m/s)(60\ s)\\`

m₁ = 12600 kg

c)

`m_1 = \rho A_1v_1t`

where,

m₂ = mass of water flowing out = ?

ρ = density of water = 1000 kg/m³

t = time = 1 min = 60 s

Therefore,

`m_2 = (1000\ kg/m^3)(0.007\ m^2)(30\ m/s)(60\ s)\\`

m₂ = 12600 kg