Two small liquid-propellant rocket motors are mounted at the tips of a helicopter rotor

Identify the surface and body forces acting on a glider in flight. Also, sketch a free body diagram and explain how Newton's laws of motion apply.

Newton's second law can be stated that the force is equal to the rate of change of momentum, F = d(mv)!dt. Taking the derivative by parts yields F = m(dv)!(dt) + v(dm)l(dt). This does not correspond to F = rna. What is the source of the discrepancy?

Which are the following are correct with respect to the derivation of the momentum equation? (Select all that apply.) a. Reynold's transport theorem is applied to Pick's law. b. The extensive property is momentum. c. The intensive property is mass. d. 1 he velocity is assumed to be uniformly distributed across each inlet and outlet. e. The net momentum flow is the "ins" minus the "outs: f. The net force is the sum of forces acting on the matter inside the CV

When making a force diagram (FlJ) and its partner momentum diagram (MD) to set up the equations for a momentum equation problem (see Fig. 6.10 on p. 217 in 6.3), which of the following elements should be in the FD, and which should be in the MD? (Classify all below a~ either FD or MlJ.) a. Each mass stream with product trr0 V0 or product rn,v; crossing a control surface boundary. b. Reaction forces required to hold walls, vanes, or pipes in place. c. Weight of a solid body that contains or contacts the fluid. d. Weight of the fluid. e. Pressure force caused by a fluid flowing across a control surface boundary.

Give five examples of jets and how they are used in practice

A "balloon rocket" is a balloon suspended from a taut wire by a hollow tube (drinking straw) and string. 1he nozzle is formed of a 0.8-cm-diameter tube, and an air jet exits the nozzle with a speed of 45 m/s and a density of 1.2 kg/m3 Find the force F needed to hold the balloon stationary. Neglect friction.

The balloon rocket is held in place by a force F. The pressure inside the balloon is 8 in-II20, the nozzle diameter is 1.0 em, and the air density is 1.2 kglm 1 . Find the exit velocity v and the force F. Neglect friction and assume tl1e air flow is inviscid and irrotational.

For Example 6.2 in 6.4, the situation diagram shows concrete being "shot" at an angle into a cart that is tethered by a cable, and sitting on a scale. Determine whether the following two statements are "true" or "false:' a. Mass is being accumulated in the cart. b. Momentum is being accumulated in the cart.

A water jet of diameter 30 mm and speed v = 25m/sis filling a tank. The tank has a mass of25 kg and contains 25liters of water at the instant shown. The water temperature is l5C. Find the force acting on the bottom of the tank and the force acting on the stop block. Neglect friction.

A design contest features a submarine that will travel at a steady speed of Vsub = I m/s in ISC water. The sub is powered by a water jet. This jet is created by drawing water from an inlet of diameter 2S mm, passing this water through a pump and then accelerating the water through a nozzle of diameter S mm to a speed of~ ,. The hydrodynamic drag force (F0 ) can be calculated using F = C (pv;ub)A D D 2 p where the coefficient of drag is C0 = 0.3 and the projected area is Ap = 0.28 m2 . Specify an acceptable value of v,.1

A horizontal water jet at 70F impinges on a verticalperpendicular plate. The discharge is 2 cfs.lf the external force required to hold the plate in place is 200 lbf, what is the velocity of the water?

A horizontal water jet at 70F issues from a circular orifice in a large tank. The jet strikes a vertical plate that is normal to the axis of the jet. A force of 600 lbf is needed to hold the plate in place against the action of the jet. If the pressure in the tank is 2S psig at point A, what is the diameter of the jet just downstream of the orifice?

An engineer, who is designing a water toy, is making preliminary calculations. A user of the product will apply a force F1 that moves a piston (D = 80 mm) at a speed of VP"'"" = 300 mm/s. Water at 20C jets out of a converging nozzle of diameter d = 15 mm. To hold the toy stationary, the user applies a force F2 to the handle. Which force (F1 versus F2) is larger? Explain your answer using concepts of the momentum principle. Then calculate F1 and F2 Neglect friction between the piston and the walls.

A firehose on a boat is producing a 4-in.-diameter water jet with a speed of V = 60 mph. The boat is held stationary by a cable attached to a pier, and the water temperature is S0F. Calculate the tension in the cable.

A boat is held stationary by a cable attached to a pier. A firehose directs a spray of SC water at a speed of V = SO m/s. If the allowable load on the cable is 5 kN, calculate the mass flow rate of the water jet. What is the corresponding diameter of the water jet?

A group offriends regularly enjoys white-water rafting, and they bring piston water guns to shoot water from one raft to another. One summer they notice that when on placid slack water (no current), after just a few volleys at each other, they are drifting apart. They wonder whether the jet being ejected out of a piston gun has enough momentum to force the shooter and raft backward. To answer this question, a. Sketch a CV, an FIJ, and an MD for this system. b. Calculate the momentum flux (N) generated by ejecting water with a flow rate of I galls from a cross section of 1.5 in.

A tank of water (l5C} with a total weight of200 N (water plus the container) is suspended by a vertical cable. Pre~surized air drives a water jet (d = 12 mm) out the bottom of the tank such that the tension in the vertical cable is 10 N. If H = 42S mm, find the required air pressure in units of atmospheres (gage). Assume the flow of water is irrotational.

A jet of water ( 60F) is discharging at a constant rate of 2.0 cfs from the upper tank.lf the jet diameter at section 1 is 4 in., what forces wil.l be measured by scales A and B? Assume the empty tank weighs 300 lbf, the cross-sectional area of the tank is 4 ft 2 , h = I ft, and H = 9ft.

The semicircular nozzle sprays a sheet of liquid through 180 of arc as shown. 'Lhe velocity is Vat the efflux section where the sheet thickness is I. Derive a formula for the external force F (in they-direction) required to hold the nozzle system in place. This force should be a function of p, V, r, and t.

The expansion section of a rocket nozzle is often conical in shape, and because the now diverges, the thrust derived from the nozzle is less than it would be if the exit velocity were everywhere parallel to the nozzle axis. By considering the flow through the spherical section suspended by the cone and assuming that the exit pressure is equal to the atmospheric pressure, show that the thrust is given by . (I + cosa) T= mV---- c 2 where r'n is the mass flow through the nozzle, V, is the exit velocity, and a is the nozzle half-angle.

Detem1ine the external reactions in the x- andy-directions needed to hold this fixed vane, which turns the oil jet (S = 0.9) in a horizontal plane. Here VI is 22 m/s, v2 = 21 m/s, and Q = 0.15 m3 / S. r U1l (S ~ 0.90) l'ROBI.I .Vt~ 6 2.~. 6.2~

Solve Prob. 6.23 for V1 = 70 ft/s, V2 = 65 ft/s, and Q = 1.5 cfs.

This planar water jet (60F) is deflected by a fixed vane. What are the x- andy-components of force per unit width needed to hold the vane stationary? Neglect gravity.

A water jet with a speed of 30ft/sand a mass flow rate of 35lbm/s is turned 30 by a fixed vane. Find the force of the water jet on the vane. Neglect gravity.

Water (p = 1000 kg/m ) strikes a block as shown and is deflected 30. The flow rate of the water is 1.5 kg/s, and the inlet velocity is V = 10 m/s. The mass of the block is I kg. The coefficient of static friction between the block and the surface is 0.1 (friction force/normal force). If the force parallel to the surface exceeds the frictional force, the block will move. Determine the force on the block and whether the block will move. Neglect the weight of the water.

For the situation described in Prob. 6.27, find the maximum inlet velocity (V) such that the block will not slip.

Plate A is 50 em in diameter and has a sharp-edged ori~ce at its center. A water jet (at !0C) strikes the plate concentrically with a speed of 90 m/s. What external force is needed to hold the plate in place if the jet issuing from the orifice also has a speed of 90 m/s? n1e diameters of the jets arc D - I 0 em and d = 3.5 em.

A cone that is held stable by a wire is free to move in the vertical direction and has a jet of water (at I 0C) striking it from below. The cone weighs 30 N. The initial speed of the jet as it comes from the orifice is IS m/s, and the initial jet diameter is 2 em. Find the height to which the cone will rise and remain stationary. Note: The wire is only for stability and should not enter into your calculations.

A horizontal jet of water (at l0C) that is 6 em in diameter and has a velocity of 20 m/s is deflected by the vane as shown. Tf the vane is moving at a rate of 7 mls in the x-direction, what components of force are exerted on the vane by the water in the x- andy-directions? Assume negligible friction between the water and the vane.

A vane on this moving cart deflects a IS-emdiameter water (p = 1000 kg/m3 ) jet as shown. The initial speed of the water in the jet is 50 m/s, and the cart moves at a speed of 3 m/s. If the vane splits the jet so that half goes one way and half the other, what force is exerted on the vane by the water?

Refer to the carl of Prob. 6.33. Tf the cart speed is constant at 5 ft/s, and if the initial jet speed is 60 ft/s, and jet diameter= 0.15 ft, what is the rolling resistance of the cart? (p = 62.41bm/ft 1 )

The water (p = 1000 kg/m3 ) in this jet has a speed of 60 m/s to the right and is deflected by a cone that is moving to the left with a speed of 5 m/s. The diameter of the jet is 10 em. Determine the external horizontal force needed to move the cone. Assume negligible friction between the water and the vane.

This two-dimensional water (at 50F) jet is deflected by the two-dimensional vane, which is moving to the right with a speed of 60 ft/s. The initial jet is 0.30 ft thick (vertical dimension), and its speed is 100 ft/s. What power per foot of the jet (normal to the page) is transmitted to the vane?

Assume that the scoop shown, which is 20 em wide, is used as a braking device for studying deceleration effects, such as those on space vehicles. Tf the scoop is attached to a 1000 kg sled that is initially traveling horizontally at the rate of 100 m/s, what will be the initial deceleration of the sled? The COOp dips into the water 8 em (d = 8 em). (T = l0C.)

This snowplow "cleans" a swath of snow that is 4 in. deep (d = 4 in.) and 2ft wide (B = 2 ft). The snow leaves the blade in the direction indicated in the sketches. Neglecting friction between the snow and the blade, estimate the power required for just the snow removal if the speed of the snowplow is 40 ft/s.

A finite span alrfoil can be regarded as a vane as shown in the figure. "The cross section of air affected is equal to the circle with the diameter of the wing span, b. The wing deflects the air by an angle a and produces a force normal to the free-stream velocity, the lift L, and in the free-stream direction, the drag D. The airspeed is unchanged. Calculate the lift and drag for a 30ft wing span in a 300 ft/s airstream at 14.7 psia and 60F for flow deflection of2.

Firehoses are fitted with special nozzles. Use the Internet or contact your local fire department to find information on operational conditions and typical hose and nozzle sizes used.

High-speed water jets are used for speciality cutting applications. The pressure in the chamber is approximately 60,000 psig. Using the Bernoulli equation, estimate the water speed exiting the nozzle exhausting to atmospheric pressure. Neglect compressibility effects and assume a water temperature of 60F.

Water at 60F flows through a nozzle that contracts from a diameter of 3 in. to 1 in. "fl1e pressure at section 1 is 2500 psfg, and atmospheric pressure prevails at the exit of the jet. Calculate the speed of the flow at the nozzle exit and the force required to hold the nozzle stationary. Neglect weight.

Water at 15C flows through a nozzle that contracts from a diameter of 10 em to 2 em. The exit speed is v2 = 25 m/s, and atmospheric pressure prevails at the exit of the jet. Calculate the pressure at section 1 and the force required to hold the nozzle stationary. Neglect weight.

Water (at 50f) flows through this nozzle at a rate of 20 cfs and discharges into the atmosphere. D1 = 26 in., and D2 = 9 in. Determine the force required at the flange to hold the nozzle in place. Assume irrotational flow. Neglect gravitational forces.

Solve Prob. 6.45 using the fo!Iowing values: Q = 0.30 m3 /s, D1 = 30 em, and D2 = I 0 em. (p = 1000 kg/m3 .)

This"double" nozzle discharges water {p = 62.41bm/ff) into the atmosphere at a rate of 16 cfs. If the nozzle is lying in a horizontal plane, what x-component of force acting through the flange bolts is required to hold the nozzle in place? Note: Assume irrotational flow, and assume the water speed in each jet to be the same. Jet A is 4 in. in diameter, jet B is 4.5 in. in diameter, and the pipe is 1 ft in diameter.

This "double" nozzle discharges water (at l0C) into the atmosphere at a rate of 0.65 m3 /s. If the nozzle is lying in a horizontal plane, what x-component of force acting through the flange bolts is required to hold the nozzle in place? Note: Assume irrotational flow, and assume the water speed in each jet to be the same. Jet A is 8 em in diameter, jet B is 9 em in diameter, and the pipe is 30 em in diameter.

A rocket-nozzle designer is concerned about the force required to hold the nozzle section on the body of a rocket. The nozzle section is shaped as shown in the figme. The pressure and velocity at the entrance to the nozzle are 1.5 MPa and 100 m/s. The exit pressure and velocity are 80 kPa and 2000 m/s. The mass flow through the nozzle is 220 kgls. 1l1e atmospheric pressure is 100 kPa. The rocket is not accelerating. Calculate the force on the nozzle-chamber connection. Note: The given pressures are absolute.

Water (p = 62.4lbm/ft3 ) is discharged from the twodimensional slot shown at the rate of 8 cfs per foot of slot. Determine the pressure pat the gage and the water force per foot on the vertical end plates A and C. The slot and jet dimensions B and bare 8 in. and 4 in., respectively.

Water (at l0C} is discharged from the two-dimensional slot shown at the rate of 0.40 m3 /s per meter of slot. Determine the pressure p at the gage and the water force per meter on the vertical end plates A and C. The slot and jet dimensions R and b are 20 em and 7 em, respectively.

This spray head discharges water (p = 62.4 lbm/ft1 ) at a rate of 4 ft3 /s. Assuming irrotational flow and an efflux speed of 65 ft/s in the free jet, determine what force acting through the bolts of the flange is needed to keep the spray head on the 6 in. pipe. Neglect gravitational forces.

Two circular water (p = 62.4 lbm/fe) jets of 0.5 in. diameter (d = 0.5 in.) issue from this unusual nozzle. If the effiux speed is 80.2 ft/s, what force is required at the flange to hold the nozzle in place? The pressure in the 4 in. pipe (D = 3.5 in.) is 50 psig.

Liquid (S = 1.2) enters the "black sphere" through a 2 in. pipe with velocity of 50 ft/s and a pressure of 60 psi g. It leaves the sphere through two jets as shown. The velocity in the vertical jet is 100 ft/s, and its diameter is 1 in. The other jet's diameter is also I in. What force through the 2 in. pipe wall is required in the x- andy-directions to hold the sphere in place? Assume the sphere plus the liquid inside it weighs 200 lbf.

Liquid (S = 1.5) enters the "black sphere" through a 5 em pipe with a velocity of 10 m/s and a pressure of 400 kPa. It leaves the sphere through two jets as shown. The velocity in the vertical jet is 30 m/s, and its diameter is 25 mm. The other jet's diameter is also 25 mm. What force through the 5 em pipe wall is required in the x- andy-directions to hold the sphere in place? Assume the sphere plus the liquid inside it weighs 600 N.

A hot gas stream enters a uniform-diameter return bend as shown. The entrance velocity is 100 ft/s, the gas density is 0.02lbm/tr, and the mass flow rate is 1 lbm/s. Water is sprayed into the duct to cool the gas down. The gas exits with a density of 0.06 lbm/ft3 . The mass flow of water into the gas is negligible. The pressures at the entrance and exit are the same and equal to the atmospheric pressure. Find the force required to hold the bend.

Assume that the gage pressure p is the same at sections 1 and 2 in the horizontal bend shown in the figure. The fluid flowing in the bend has density p, discharge Q, and velocity V. The cross-sectional area of the pipe is A. Then the magnitude of the force (neglecting gravity) required at the flanges to hold the bend in place will be (a) pA, (b) pA + pQV, (c) 2pA + pQV, or (d) 2pA + 2pQV.

The pipe shown has a 180 vertical bend in it. The dian1eter Dis 1 ft, and the pressure at the center of the upper pipe is 15 psig. If the flow in the bend is 20 cfs, what external force will be required to hold the bend in place against the action of the water? The bend weighs 200 lbf, and the volume of the bend is 3 ft3 . Assume the Bernoulli equaliC'n applies. (p = 62.4 lbm/ft3 .)

Set up the solution for Problem 6.60, and answer the following questions: a. Do the two pressure forces from the inlet and exit act in the same direction, or in opposite directions? b. for the data given, which term has the larger magnitude (in N), the pressure force term, or the net momentum flux term?

Water (at 50F) flows in the 90 horizontal bend at a rate of 12 cfs and discharges into the atmosphere past the downstream flange. The pipe diameter is 1 ft. What force must be applied at the upstream flange to hold the bend in place? Assume that the volume of water downstream of the upstream flange is 4 ft3 and that the bend and pipe weigh 100 lbf. Assume the pressure at the inlet section is 4 psig.

The gage pressure throughout the horizontal90 pipe bend is 300 kPa. If the pipe diameter is 1 m and the water (at l0C) flow rate is 10 m3 /s, what x-component of force must be applied to the bend to hold it in place against the water action?

This 30 vertical bend in a pipe with a 2ft diameter carries water (p = 62.4 lbm/ft3 ) at a rate of 31.4 cfs. If the pressure p1 is 10 psi at the lower end of the bend, where the elevation is 100 ft, and p2 is 8.5 psi at the upper end, where the elevation is 103 ft, what will be the vertical component of force that must be exerted by the "anchor" on the bend to hold it in position? The bend itself weighs 300 lb, and the length Lis 4ft.

This bend discharges water (p = 1000 kg/m3 ) into the atmosphere. Determine the force components at the flange required to hold the bend in place. The bend lies in a horizontal plane. Assume viscous forces are negligible. The interior volume of the bend is 0.25 m3 , Dt = 60 em, D2 = 30 em, and V2 = 10 m/s. The mass of the bend material is 250 kg.

This nozzle bends the flow from vertically upward to 30 with the horizontal and discharges water ( 'Y = 62.4lbf/ft3 ) at a speed of V = 130 ft/s. The volume within the nozzle itself is 1.8 ftl, and the weight of the nozzle is 100 lbf. For these conditions, what vertical force must be applied to the nozzle at the flange to hold it in place?

A pipe 1 ft in diameter bends through an angle of 135. The velocity of flow of gasoline (S = 0.8) is 20 ft/s, and the pressure is 10 psig in the bend. What external force is required to hold the bend against the action of the gasoline? Neglect the gravitational force.

A 6 in. horizontal pipe has a 180 bend in it. If the rate of flow of water (60F) in the bend is 2 cfs and the pressure therein is 20 psig, what external force in the original direction of flow is required to hold the bend in place?

A pipe 15 em in diameter bends through 135. The velocity of flow of gasoline (S = 0.8) is 8 m/s, and the pressure is 100 kPa gage throughout the bend. Neglecting gravitational force, determine the external force required to hold the bend against the action of the gasoline.

Water (at 10C) flows in a duct as shown. The inlet water velocity is 10 m/s. The cross-sectional area of the duct is 0.1 m2 Water is injected normal to the duct wall at the rate of 500 kg/s midway between stations 1 and 2. Neglect frictional forces on the duct wall. Calculate the pressure difference (p 1 - p 2) between stations I and 2.

For this wye fitting, which lies in a horizontal plane, the cross-sectional areas at sections I, 2, and 3 are I ft2 , 1 ft2 , and 0.25 fe, respectively. At these same respective sections the pressures are 1000 psfg, 900 psfg, and 0 psfg, and the water discharges are 20 cfs to the right, 12 cfs to the right, and exits to atmosphere at 8 cfs. What x-component of force would have to be applied to the wyc to hold it in place?

Water (p = 62.4lbm/ft3 ) flows through a horiwntal bend and T section as shown. The mass flow rate entering at section a is 12lbm/s, and those exiting at sections band care 6lbm/s each. The pressure at section a is 5 psi g. The pressure at the two outlets is atmospheric. The cross-sectional areas of the pipes are the same: 5 in2 . Find the x-component of force necessary to restrain the section.

Water (p = 1000 kg/ m3 ) flows through a horizontal bend and T section as shown. At section a the flow enters with a velocity of 6 m/s, and the pressure is 4.8 kPa. At both sections b and c the flow exits the device with a velocity of 3 m/s, and the pressure at these sections is atmospheric (p = 0). The crosssectional areas at a, b, and care all the same: 0.20 m2 Find the x- andy-components of force necessary to restrain the section.

For this horizontal T through which water (p = 1000 kg!m3 ) is flowing, the following data arc given: Q1 = 0.25 m3 /s, Q2 = 0.10 m3 /s, p 1 = 100 kPa,p2 = 70 kPa,p3 = 80 kPa, D 1 = I 5 em, D2 = 7 em, and D3 = 15 em. For these conditions, what external force in the x-y plane (through the bolts or other supporting devices) is needed to hold the Tin place?

Firehoses can break windows. A 0.2-m diameter (D1) firehose is attached to a nozzle with a 0.1 m diameter (d2) outlet. The free jet from the nozzle is deflected by 90 when it hits the window as shown. Find the force the window must withstand due to the impact of the jet when water flows through the firehose at a rate of 0.15 m3 /s.

A fireman is soaking a home that is dangerously close to a burning building. To prevent water damage to the inside of the neighboring home, he throttles down his flow rate so that it will not break windows. Assuming the typical window should be able to withstand a force up to 25 lbf, what is the largest volumetric flow rate he should allow (gal/min.), given an 8-inch diameter (D1) firehose discharging through a nozzle with 4-inch diameter (d2) outlet. 1be free jet from the nozzle is deflected by 90 when it hits the window as shown.

For laminar flow in a pipe, wall shear stress (-r0) causes the velocity distribution to change from uniform to parabolic as shown. At the fully developed section (section 2), the velocity is distributed as follows: u = Umax ll - (r/r0) 2 ]. Derive a formula for the force on the wall due to shear stress, FT. between 1 and 2 as a function of U (the mean velocity in the pipe), p,p1,p2, and D (the pipe diameter).

The propeller on a swamp boat produces a slipstream 3ft in diameter with a velocity relative to the boat of 100 ft/s.If the air temperattrre is 80F, what is the propulsive force when the boat is not moving and also when its forward speed is 30 ft!s? Hint: Assume that the pressure, except in the immediate vicinity of the propeller, is atmospheric.

The figure illustrates the principle of the jet pump. Derive a formula for p2 - p 1 as a function of D1, ~ D0, V0, and p.Assume that the fluid from the jet and the fluid initiaiiy flowing in the pipe are the same, and assume that they are completely mixed at section 2, so that the velocity is uniform across that section. Also asswne that the pressures are uniform across both sections I and 2. What is p2 - p1 if the fluid is water, A/ Ao = 1/3, ~ = IS m/s, and V0 = 2 m/s? Neglect shear stress.

Jet-type pumps are sometimes used to circulate the flow in basins in which fish are being reared. The use of a jet-type pump eliminates the need for mechanical machinery that might be injurious to the fish. -nle accompanying figure shows the basic concept for this type of application. for this type of basin the jets would have to increase the water surface elevation by an amount equal to 6 V2 /2g, where Vis the average velocity in the basin (1 ft/s as shown in this example). Propose a basic design for a jet system that would make such a recirculating system work for a channel 8ft wide and 4 ft deep. That is, determine the speed, size, and number of jets.

An engineer is measuring the lift and drag on a wind turbine blade section mounted in a two-dimensional wind tunnel.l11e wind tunnel is 0.5 m high and 0.5 m deep (into the paper). The upstream wind velocity is uniform at 10 m/s, and the downstream velocity is 12 m/s and 8 m/s as shown. The vertical component of velocity is zero at both stations. 'I he test section is I m long. 'lhe engineer measures the pressure distribution in the tunnel along the upper and lower walls and finds p., = 100 - lOx - 20x( I - x)(Pa gage) P1 = 100 - lOx + 20x(J - x)(Pa gage) where xis the distance in meters measured from the beginning of the test section. The gas density is homogeneous throughout and equal to 1.2 kg/m3 The lift and drag are the vectors indicated on the figure. The forces acting on the fluid are in the opposite direction to these vectors. Find the lift and drag forces acting on the wind turbine blade section.

A torpedolike device is tested in a wind tunnel with an air density of 0.0026 slugs/ft3 . The tunnel is 3ft in diameter, the upstream pressure is 0.24 psig, and the downstream pressure is 0.10 psig.lf the mean air velocity Vis 120 ft/s, what are the mass rate of flow and the maximum velocity at the downstream section at C? If the pressure is assumed to be uniform across the sections at A and C, what is the drag of the device and support vanes? Assume viscous resistance at the walls is negligible

A ramjet operates by taking in air at the inlet, providing fuel for combustion, and exhausting the hot air through the exit. The mass flow at the inlet and outlet of the ramjet is 60 kg/s (the mass flow rate of fuel is negligible). The inlet velocity is 225 m/s. The density of the gases at the exit is 0.25 kg/m ', and the exit area is 0.5 m2 Calculate the thrust delivered by the ramjet. The ramjet is not accelerating, and the flow within the ramjet is steady.

A modern turbofan engine in a commercial jet take~ in air, part of which passes through the compressors, combustion chambers, and turbine, and the rest of which bypasses the compressor and is accelerated by the fans. The mass flow rate of bypass air to the mass flow rate through the compressor-combustor-turbine path is called the "bypass ratio. The total flow rate of air entering a turbofan is 300 kg!s with a velocity of 300 m/s. The engine has a bypass ratio of 2.5. The bypass air exits at 600 m/s, whereas the air through the compressor- combustor-turbine path exits at 1000 m/s. What is the thrust of the turbofan engine? Clearly show your control volume and application of momentum equation.

Using the Internet or some other source as reference, define in your own words the meaning of"inertial reference frame:'

The surface of the earth is not a true inertial reference frame because there is a centripetal acceleration due to the earth's rotation. The earth rotates once every 24 hours and has a diameter of 8000 miles. What is the centripetal acceleration on the surface of the earth, and how does it compare to the gravitational acceleration?

A large tank of liquid is resting on a frictionless plane as shown. Explain in a qualitative way what will happen after the cap is removed from the short pipe.

Consider a tank of water (p = 1000 kg/m3 ) in a container that rests on a sled. A high pressure is maintained by a compressor so that a jet of water leaving the tank horizontally from an orifice does so at a constant speed of 25 m/s relative to the tank. If there is 0.10 m3 of water in the tank at timet and the diameter of the jet is IS mm, what will be the acceleration of the sled at timet if the empty tank and compressor have a weight of 350 N and the coefficient of friction between the sled and the ice is 0.05?

A cart is moving along a railroad track at a constant velocity of 5 m/s as shown. Water (p = 1000 kg!m') issues from a nozzle at 10 rn/s and is deflected through 180 by a vane on the cart. The cross-sectional area of the nozzle is 0.002 m2 . Calculate the resistive force on the cart.

A water jet is used to accelerate a cart as shown. The discharge (Q) from the jet is 0.1 m3 /s, and the velocity of the jet('\.';) is 10 m/s. When the water hits the cart, it is deflected normally as shown. The mass of the cart (M) is 10 kg. The density of water (p) is 1000 kg/m 3 .1l1ere is no resistance on the cart, and the initial velocity of the cart is zero. The mass of the water in the jet is much less than the mass of the cart. Derive an equation for the acceleration of the cart as a function of Q, p. ~. M, and V;. Evaluate the acceleration of the cart when the velocity isS m/s.

A water jet strikes a cart as shown. After striking the cart, the water is deflected vertically with respect to the cart. The cart is initially at rest and is accelerated by the water jet. The mass in the water jet is much less than that of the cart. There is no resistance on the cart. The mass flow rate from the jet is 4S kgls. The mass of the cart is I 00 kg. Find the time required for the cart to achieve a speed one-half of the jet speed.

It is common practice in rocket trajectory analyses to neglect the body-force term and drag, so the velocity at burnout is given by T Mo V00 =-In- >-. Ml Assuming a thrust-to-mass-flow ratio of 3000 N s/kg and a final mass of SO kg, calculate the initial mass needed to establish the rocket in an earth orbit at a velocity of 7200 m/s.

A very popular toy on the market several years ago was the water rocket. Water (at 1 0C) was loaded into a plastic rocket and pressurized with a hand pump. The rocket was released and would travel a considerable distance in the air. Assume that a water rocket has a mass of SO g and is charged with 100 g of water. The pressure inside the rocket is 100 kPa gage. The exit area is one-tenth of the chamber cross-sectional area. The inside diameter of the rocket is S em. Assume that Bernoulli's equation is valid for the water flow inside the rocket. Neglecting air ==::o=::==~~--~ friction, calculate the maximum velocity it will attain.

Water (p = I 000 kg/m3 ) is discharged from the slot in the pipe as shown. If the resulting two-dimensional jet is 100 em long and 1S mm thick, and if the pressure at section A-A is 30 kPa, what is the reaction at section A-A? In this calculation, do not consider the weight of the pipe.

Two small liquid-propellant rocket motors are mounted at the tips of a helicopter rotor to augment power under emergency conditions. The diameter of the helicopter rotor is 7 m, and it rotates at 1 rev/s. The air enters at the tip speed of the rotor, and exhaust gases exit at SOO m/s with respect to the rocket motor. The intake area of each motor is 20 cm2 , and the air density is 1.2 kg/m3 . Calculate the power provided by the rocket motors. Neglect the mass rate of Aow of fuel in this calculation.

What is the force and moment reaction at section I? Water (at 50f) is flowing in the system. Neglect gravitational forces.

A reducing pipe bend is held in place by a pedestal as shown. There are expansion joints at sections I and 2, so no force is transmitted through the pipe past these sections. The pressure at section 1 is 20 psig, and the rate of flow of water (p = 62.4lbm/ftl) is 2 cfs. Find the force and moment that must be applied at section 3 to hold the bend stationary. Assume the flow is irrotational, and neglect the influence of gravity.

A centrifugal fan is used to pump air. The fan rotor is 1ft in diameter, and the blade spacing is 2 in. The air enters with no angular momentum and exits radially with respect to the fan rotor. The discharge is 1500 cfm. The rotor spins at 3600 rev/min. The air is at atmospheric pressure and a temperature of 60F. Neglect the compressibility of the air. Calculate the power (hp) required to operate the fan.