143k views
4 votes
Q1) A pipe of radius 0.6 cm discharges petrol at a rate of 2.45 m/s. Find the volume of petrol discharged in 3 minutes, giving your answer in litres.

Q2) A pipe diameter 0.036 m discharges water at a rate of 1.1 m?s into a cylindrical tank with a base radius of 3.4 m and height of 1.4 m. Find the time required to fill the tank giving your answer correct to the nearest minute.

User Sudi
by
7.4k points

1 Answer

14 votes

Answer:

Q1) The volume of petrol discharged in 3 minutes is approximately 49.88 litres

Q2) The time it takes to fill the tank is approximately 12 hours 37 minutes

Explanation:

Q1) The flow rate of fluid from a pipe, 'Q' is given according to the following equation;


Q = (V)/(t) =(A \cdot l)/(t) = A \cdot \overline v

Where;

Q = The flow rate of fluid in the pipe

V = The volume that flows from the pipe in the given time

A = The cross sectional area of the pipe

t = The time it takes a given volume of fluid to flow from the pipe

l = The length of the pipe that the volume that flows in the given time takes in the pipe


\overline v = The rate at which the fluid flows

For a circular pipe, A = π·r²

r = The radius of the pipe

The given parameters in the question are;

r = 0.6 cm = 0.006 m


\overline v = 2.45 m/s

Therefore, by plugging in the values, we get;

A = π·r² = π × (0.006 m)²

Q = A·
\overline v = (π × (0.006 m²)) × 2.45 m/s

Q = (π × (0.006 m²)) × 2.45 m/s

V = Q × t

Where;

t = Time of flow = 3 minutes = 3 minutes × 60 seconds/minute = 180 seconds

t = 180 s

∴ V = Q × t = ((π × (0.006 m²)) × 2.45 m/s) × 180 s = 0.04987592496 m³

V = 0.04987592496 m³

1 m³ = 1,000 l

∴ 0.04987592496 m³ = 0.04987592496 m³ × 1,000 l/m³= 49.87592496 l

∴ V = 0.04987592496 m³ = 49.87592496 l ≈ 49.88 litres

The volume of petrol discharged in 3 minutes, V ≈ 49.88 litres

Q2) The given diameter of the pipe, d = 0.036 m

The rate at which water discharges into the cylindrical tank,
\overline v = 1.1 m/s

The base radius of the cylindrical tank, R = 3.4 m

The height of the cylindrical tank, h = 1.4 m

Therefore, we have;

The radius of the pipe, r = d/2 = 0.036 m/2 = 0.018 m

The cross sectional area of the pipe, A = π·r² = π×( 0.018 m)²

The volume of the cylindrical tank, V = (The base area of the tank) × (The height of the tank)

∴ V = π × R² × h = π × (3.4 m)² × 1.4 m = π·16.184 m³

The flow rate of Q = A ×
\overline v = (π×( 0.018 m)²) × 1.1 m/s = π·0.0003564 m³/s

Q = V/t

∴ t = V/Q

Where;

t = The time it takes to fill a volume, 'V', at a flow rate 'Q'

∴ t = V/Q = (π·16.184 m³)/(π·0.0003564 m³/s) = 45409.6520763 s

t = 45409.6520763 s = 12 hours 36 minutes 49 seconds (using an online time converter)

Therefore, The time it takes to fill the tank, t ≈ 12 hours 37 minutes, after rounding to the nearest minute.

User Flxkid
by
8.1k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories