Randall D. Knight — Fluids and Elasticity: Problem Exercise_33

FIGURE EX14.33 shows a syringe filled with 20°C olive oil. What is the gauge pressure at point P where the needle meets the wider body of the syringe? Give your answer in atm. Given parameters from Figure EX14.33: Radius of syringe barrel: \(R_{\text{barrel}} = 1.0 \text{ cm}\) Radius of needle: \(R_{\text{needle}} = 1.0 \text{ mm}\) Length of needle: \(L = 4.0 \text{ cm}\) Velocity at needle exit: \(v_{\text{needle}} = 2.0 \text{ m/s}\) Fluid: Olive oil at 20°C (\(\rho = 920 \text{ kg/m}^3\), \(\eta = 0.084 \text{ Pa}\cdot\text{s}\))