The flow rate of the IV pump should be 17.06mL/hr.
1st) We need to calculate the patient's weight knowing that 1 lb is equal to 0.45 kg:
[tex]\begin{gathered} 1\text{ lb-0.45 kg} \\ 237\text{ lb - x =}\frac{237\text{ lb}\cdot\text{0.45 kg}}{1\text{ lb}} \\ \\ x=106.65\operatorname{kg} \end{gathered}[/tex]
The patient weighs 106.65 kg.
2nd) If the patient needs a drip at 8.0 units per kg of body weight, we have to calculate the units for the patient:
[tex]\begin{gathered} 1\text{ kg - 8.0 units} \\ 106.65\text{ kg - x=}\frac{106.65\text{ kg}\cdot\text{8.0 units}}{1\text{ kg }} \\ \\ x=853.2\text{units} \end{gathered}[/tex]
So, the patient needs 853.2 units per hour.
3rd) To calculate the flow rate of the IV pump, we need to know the mL equivalent to 853.2 units:
[tex]\begin{gathered} 25,000\text{ units - 500mL} \\ 853.2\text{ units - x=}\frac{853.2\text{ units}\cdot\text{500mL}}{25,000\text{ units}} \\ \\ x=17.06mL \end{gathered}[/tex]
So, the flow rate of the IV pump should be 17.06mL/hr.