Can somebody please help me with these physics questions?

Question

1.) A bug from South America known as Rhodnius prolixus extracts the blood of animals. Suppose Rhodnius prolixus extracts 0.300 cm³ of blood in 25.0 min from a human arm through its feeding tube of length 0.200 mm and radius 5.00 μm. What is the absolute pressure at the bug’s end of the feeding tube if the absolute pressure at the other end (in the human arm) is 106 kPa? Assume the viscosity of blood is 0.00130 Pa·s. Give answer in kPa.

2.) Water enters an apartment building 0.900 m below the street level with a gauge pressure of 52.0 kPa through the main pipe, which has a 5.00 cm radius. A second-story bathroom has an open faucet with a 1.20 cm radius that is located 3.30 m above the street. How fast is the water moving through the main pipe? Density of water is 1.00 × 10³ kg/m³.

Answer 1

in 1) You need to use the Poiseuille equation for a volumetric flow throw a pipe: Q =(π/8L)*(ΔPr⁴/μ)

Solve for ΔP = 8LQμ/(πr⁴). Now put everything in MKS and you will get P in Pascals (/1000 for kPa)

The absolute P at the bug will be 106 kPa - ΔP.

Q = .3 cm³/35 min *(1 min/60 s) *(1 m/10² cm)³ = 1.667 x 10^-9 m³/s

r = 5 x 10^-6 m and μ is in the right units.

in 2) You need Bernoulli's Equation and the continuity equation

The Bernoulli Equation (divided by density) = 1/2 v_m² + gy_m + P_m^/ρ = 1/2 v_f² + gy_f + P_f/ρ

The continuity equation says that v_mA_m = v_fA_f or that v_f/v_m = (r_m/r_f)² after substituting πr² for A and rearranging.

1/2 v_m² + gy_m + P_m^/ρ = 1/2 v_m²(r_m²/r_f²) + gy_f + P_f/ρ Subbing in continuity

1/2 v_m² + gy_m + P_m,G^/ρ = 1/2 v_m²(r_m⁴/r_f⁴) + gy_f Where P_m = P_m,g + P_atm and P_f = P_atm

v_m = sqrt((2*(g(y_f-y_m) - P_m,G/ρ)/(1-r_m⁴/r_f⁴)) Rearranging and solving for v_m

Plug in with radii in meters.