Sharks are fish, and as such, they have a closed circulatory system (the blood never leaves the web of blood vessels). The blood is pumped through a singular loop throughout the body, to transport nutrients, gases, hormones, blood cells, nitrogen waste products, etc. back and forth through cells in the body. These nutrients help fight disease and stabilize body temperature/pH in order to maintain homeostasis. The blood travels from the two chambered heart (one atrium and one ventricle) to the gills, after which it is transported throughout the whole body, and finally back to the heart.
The heart of a shark contains four parts, the aforementioned atrium and ventricle, the sinus venosus, and the bulbus arteriosus. The sinus venosus is a small sac with thin walls which collects deoxygenated blood from the fish's veins, after which the blood flows into the atrium, a large muscular chamber. The atrium is a one-way compartment for blood to flow into the ventricle (which does the pumping for the heart). The bulbus arteriosus is a large tube into which the blood is pumped from the ventricle. The bulbus arteriosus then leads the blood to the aorta, through which blood flows to the shark's gills - where carbon dioxide is exchanged for oxygen bubbles.
Normally, 3% to 8% of a shark's body weight is blood. The blood consists of plasma and cells (erythrocytes - red blood cells and leukocytes - white blood cells). Plasma is 80% water, which also contains a multitude of ions (such as Na+, Ca2+, and K+), and dissolved molecules such as urea, sugars and fatty acids.
Erythrocytes are most common, and move gases around the body. They deposit carbon dioxide at the gills, and obtain oxygen, which they distribute throughout the cells of the body. Hemoglobin is a pigment which makes erythrocytes red, also allowing them to carry out their job.
Leukocytes do not contain the pigment hemoglobin, and therefore are colorless. There are five types of leukocytes: (1) Granulocytes, (2) Lymphocytes, (3) Monocytes, (4) Thrombocytes, (5) Non-specific Cytotoxic Cells, each one with their own intricate functions.
If you feel a shark's pulse, there is a beat - space - beat - space - beat - space, and so on and so forth. The beat is blood being pumped out of the heart, and the space is when the ventricle relaxes and is filled with blood. The beat is called a systole, and a space is called a diastole. Together, they make one beat of the heart of a shark.