In humans, blood flows from the heart into aorta, from which it passes into major arteries These branch into the small arteries (arterioles), which in turn branch into myriads of tiny capillaries. The blood returns to the heart via the veins. The radius of the aorta is about 1.2 cm, and the blood passing through it has a speed of about 40 cm / s. A typical capillary has a radius of about 0.0004 cm, and blood flows through it at a speed of about 0.05 cm / s. Estimate the number of capillaries that are in the body

Water enters a shower head through a pipe of internal radius r = 6.4 mm, and leaves through 30 small holes, each of radius r1 = 0.08 mm. When the faucet is opened, the water moves in the tube at a speed of 90 cm/s. What is the volumetric flow of the shower head in liters per second?

A centrifugal pump has the following characteristics as shown in Table 1. Table 1: Pump characteristics Q(m3 /s) 0.033 0.029 0.027 0.0235 0.020 0.017 0.0133 H(m) 40 60 66 75 80 84 90 Efficiency % 20 45 55 68 75 66 45 The pump is used to pump water from a low reservoir to a high reservoir through a total length of 1100 m of pipe 250 mm in diameter. The difference between the water levels in the reservoirs is 25 m. Neglecting all losses except friction and assuming λ=0.042, calculate: i. The discharge and head at the duty point for the pump. (20) ii. The efficiency at the duty point. (5) [2

Fluid Mechanics  A horizontal jet of water exits a nozzle with a uniform velocity of Vj = 20 m/s and area of Aj= 3 cm^2, and strikes a flat plate that moves to the right at velocity of Vc = 15 m/s. Upon impinging the plate, the jet splits into an equal upward and downward half-jet. (i.e. A1 = A2 = 0.5Aj). Neglecting gravity and viscous forces, determine the force (in both x - and y - directions) required to keep the plate moving at a constant velocity.