GATE 2017 CE (CE1) – Question 59
Water passes through the horizontal 90° bend and nozzle shown, discharging to the atmosphere. Gauge pressure at section 1–1 is 140 kPa. Inlet diameter is $27/\sqrt\pi$ cm and nozzle diameter is $14/\sqrt\pi$ cm. Take $g=10$ m/s²; neglect the weights of water and bend, and friction across the bend. Find the holding-force magnitude in kN, to two decimal places.
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Correct answer: 2.50 to 3.75
Explanation
The areas are $A_1=0.27^2/4=0.018225$ m² and $A_2=0.14^2/4=0.0049$ m². Continuity gives $V_1=(A_2/A_1)V_2$. With $\rho=1000$ kg/m³, Bernoulli gives $V_2=\sqrt{2(140000)/[1000(1-(A_2/A_1)^2)]}=17.37$ m/s, $V_1=4.67$ m/s and $Q=0.0851$ m³/s. Momentum gives orthogonal holding-force components of magnitudes $p_1A_1+\rho QV_1\simeq2949$ N and $\rho QV_2\simeq1479$ N. Their resultant is about 3.30 kN. The broad archived interval 2.50–3.75 kN is retained.