A tank with a constant water level of 4 m above the centreline of an opening of diameter 100 mm is shown in the figure. Neglect all losses and assume \( g = 9.81 \, {m/s}^2 \). The discharge through the opening is ________ litres/s (answer in integer).
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When calculating discharge, ensure to convert units to maintain consistency, especially when converting from cubic meters to litres.
Step 1: Apply the Torricelli's law for discharge.
The discharge rate \( Q \) through an opening in the tank can be calculated using Torricelli's law:
\[
Q = A \sqrt{2 g h},
\]
where:
\( A \) is the area of the opening,
\( g \) is the acceleration due to gravity (\( 9.81 \, {m/s}^2 \)),
\( h \) is the height of the water above the centre of the opening (4 m). Step 2: Calculate the area of the opening.
The diameter of the opening is given as 100 mm, so the radius \( r \) is:
\[
r = \frac{100}{2} = 50 \, {mm} = 0.05 \, {m}.
\]
The area \( A \) of the opening is:
\[
A = \pi r^2 = \pi (0.05)^2 = 7.854 \times 10^{-3} \, {m}^2.
\]
Step 3: Calculate the discharge.
Now, substitute the values into the formula for discharge:
\[
Q = 7.854 \times 10^{-3} \times \sqrt{2 \times 9.81 \times 4}.
\]
Simplify:
\[
Q = 7.854 \times 10^{-3} \times \sqrt{78.48} = 7.854 \times 10^{-3} \times 8.86.
\]
Thus,
\[
Q \approx 0.0696 \, {m}^3/{s}.
\]
Step 4: Convert the discharge to litres per second.
Since 1 cubic meter is 1000 litres:
\[
Q = 0.0696 \times 1000 = 69.6 \, {litres/s}.
\]
Step 5: Round off the answer.
Thus, the discharge is approximately \( \boxed{70} \, {litres/s} \).
