Given a 4 m diameter round hatch placed on an inclined surface (60° to the surface of the water) for a tank filled with water. The hatch is fixed on the axis of horizontal rotation, which passes through the center along the entire length of the diameter. The axis of rotation is located 10 m under water. The hatch cannot open clockwise, as it is limited by the brake unit. Task: (a) What is the resulting force acting on the hatch? b)By what size should the moment around the axis of rotation be greater to open the lid? (Answer: a)1233 kN; (b) 106,7 kNm)

Water enters a smooth, horizontal tube with a speed of 2.0 m/s and emerges out of the tube with a speed of 8.0 m/s. Each end of the tube has a different cross-sectional radius. Find the ratio of the entrance radius to the exit radius.

A large storage tank with an open top is filled to a height h0. The tank is punctured at a height h above the bottom of the tank (Fig. P15.39). Find an expression for how far from the tank the exiting stream lands. Figure P15.39

Do fluids exert buoyant forces in a “weightless" environment, such as in the space shuttle? Explain your answer.

A fluid flows through a horizontal pipe that widens, making a 45 angle with the y axis (Fig. P15.48). The thin part of the pipe has radius R, and the fluids speed in the thin part of the pipe is v0. The origin of the coordinate system is at the point where the pipe begins to widen. The pipes cross section is circular. a. Find an expression for the speed v(x) of the fluid as a function of position for x 0 b. Plot your result: v(x) versus x. FIGURE P15.48 (a) The continuity equation (Eq. 15.21) relates the cross-sectional area to the speed of the fluid traveling through the pipe. A0v0 = A(x)v(x) v(x)=A0v0A(x) The cross sectional area is the area of a circle whose radius is y(x). The widening pan of the pipe is a straight line with slope of 1 and intercept y(0) = R. y(x) = mx + b = x + R A(x) = [y(x)]2 = (x + R)2 Plug this into the formula for the velocity. Plug this into the formula for the velocity. v(x)=A0v0(x+R)2

Fluid originally flows through a tube at a rate of 100 cm3/s. To illustrate the sensitivity of flow rate to various factors, calculate be new flow rate for following changes with all other factors remaining the same as in original conditions. (a) Pressure difference increases by a factor of 1.50. (b) A new fluid wit 3.00 times greater viscosity is substituted. (c) The tube is replaced by one having 4.00 times the length. (d) Another tube used with a 0.100 times the original. (e) Yet another tube is substituted with a radius 0.100 times the original and half length, and pressure difference is increased by factor of 1.50.

Show that the Reynolds number NRis unitless by substituting units for all the quantities in its definition and cancelling.

A spherical weather balloon is filled with hydrogen until its radius is 3.00 m. Its total mass including the instruments it carries is 15.0 kg. (a) Find the buoyant force acting on the balloon, assuming the density of air is 1.29 kg/m3. (b) What is the net force acting on the balloon and its instruments after the balloon is released from the ground? (c) Why does the radius of the balloon tend to increase as it rises to higher altitude?

A 1.00-kg beaker containing 2.00 kg of oil (density = 916.0 kg/m3) rests on a scale. A 2.00-kg block of iron suspended from a spring scale is completely submerged in the oil as shown in Figure P15.63. Determine the equilibrium readings of both scales. Figure P15.63 Problems 63 and 64.

In an immersion measurement of a woman's density, she is found to have a mass of 62.0 kg in air and an apparent mass of 0.0850 kg when completely submerged with lungs empty. (a) What mass of water does she displace? (b) What is her volume? (c) Calculate her density. (d) If her lung capacity is 1.75 L is she able to float without treading water with her lungs filled with air?