a garden hose with a diameter of 0.65 in has a water flowing in it with a speed

Question

a garden hose with a diameter of 0.65 in has a water flowing in it with a speed of 0.55m/s and a pressure of 1.2 atmospheres. at the end of the hose is a nozzle with a diameter of 0.25 in. (a) find the speed of water in the nozzle (b) the pressure in the nozzle

Explanation / Answer

Assuming incompressible flow, volumetric flow rate is constant. volumetric flow rate is average speed times cross-sectional area. v_hose · (p/4) · (d_hose)² = v_nozzle · (p/4) · (d_nozzle)² => v_nozzle = v_hose · (d_hose/d_nozzle)² = 0.55m/s · (0.65in/0.25in)² = 3.718m/s b) Assuming frictionless, incompressible flow, Bernoulli's principle states that p/? + g·z + (1/2)·v² = constant Hence: p_nozzle/? + g·z_nozzle + (1/2)·(v_nozzle)² = p_hose/? + g·z_hose + (1/2)·(v_hose)² Let hose and nozzle be at the same height: p_nozzle/? + (1/2)·(v_nozzle)² = p_hose/? + (1/2)·(v_hose)² => p_nozzle = p_hose + (1/2)·?·[(v_hose)² - (v_nozzle)²] = 1.2·101325Pa + (1/2)·1000kg/m³·[(0.55m/s)² - (3.178m/s)²] = 114829Pa = 1.133atm

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