Final answer:
The hemorrhaging client is experiencing a deficit in intravascular fluid, which necessitates a blood transfusion to replenish the intravascular volume.
Step-by-step explanation:
The client who is hemorrhaging is experiencing a deficit in intravascular fluid. Hemorrhage leads to a loss of blood, which is a major component of the extracellular fluid, specifically within the blood vessels. As blood contains plasma, which communicates with interstitial fluid, the loss during hemorrhage chiefly pertains to a decrease in blood plasma and overall intravascular volume. Therefore, in this scenario, the nurse would identify that the blood transfusion is necessary to restore the balance of fluid within the intravascular compartment.