Let's solve the problem step by step: ### **Given:** - Weight supported \( W = 100 \) N - Height \( h = 5 \) m - Velocity of water \( v = 20 \) m/s - Acceleration due to gravity \( g = 9.81 \) m/s² We are to find the diameter \( d \) of the nozzle. --- ### **Step 1: Find the mass flow rate (\(\dot{m}\))** The force (weight) supported by the jet is equal to the change in momentum per second (rate of change of momentum): \[ \text{Force} = \text{Change in momentum per second} = \dot{m} v \] \[ 100 = \dot{m} \times 20 \] \[ \dot{m} = \frac{100}{20} = 5 \text{ kg/s} \] --- ### **Step 2: Find the area of the nozzle (\(A\))** The mass flow rate is also given by: \[ \dot{m} = \rho Q = \rho A v \] Assume the density of water, \(\rho = 1000 \) kg/m³ \[ 5 = 1000 \cdot A \cdot 20 \] \[ A = \frac{5}{1000 \times 20} = \frac{5}{20000} = 0.00025 \text{ m}^2 \] --- ### **Step 3: Find the diameter (\(d\))** \[ A = \frac{\pi d^2}{4} \] \[ 0.00025 = \frac{\pi d^2}{4} \] \[ d^2 = \frac{0.00025 \times 4}{\pi} \] \[ d^2 = \frac{0.001}{3.1416} \] \[ d^2 = 0.0003183 \] \[ d = \sqrt{0.0003183} \] \[ d \approx 0.01785 \text{ m} = 17.85 \text{ mm} \] --- ### **Check the options:** - 5.12 mm - 19.14 mm - 12.32 mm Closest option is **19.14 mm**. --- ## **Final Answer:** **The diameter \( d \) of the nozzle will be:** \[ \boxed{19.14 \text{ mm}} \]