Question

Water at 45C^{\circ} \mathrm{C} enters a shower head through a circular tube with 15.8 mm inside diameter. The water leaves in 24 streams, each of 1.05 mm diameter. The volume flow rate is 5.67 L/min. Estimate the minimum water pressure needed at the inlet to the shower head. Evaluate the force needed to hold the shower head onto the end of the circular tube. Indicate whether this is a compression or a tension force.

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Given data:

Tw=45CT_w=45\mathrm{^{\circ}C}

D1=15.8mm1m1000mm=0.0158mD_1=15.8\mathrm{mm}\cdot\frac{1\mathrm{m}}{1000\mathrm{mm}}=0.0158\mathrm{m}

n=24n=24

Ds=1.05mm1m1000mm=0.00105mD_s=1.05\mathrm{mm}\cdot\frac{1\mathrm{m}}{1000\mathrm{mm}}=0.00105\mathrm{m}

Q=5.67Lmin0.001m31L60s1min=0.0000945m3sQ=5.67\mathrm{\frac{L}{min}}\cdot\frac{\frac{0.001\mathrm{m^3}}{1\mathrm{L}}}{\frac{60\mathrm{s}}{1\mathrm{min}}}=0.0000945\mathrm{\frac{m^3}{s}}

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